Comments by "Fhf Fhf" (@fhffhff) on "ВЫХОД ЕСТЬ!"
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(x²)²-3x²+1=0,x²=(3±√(9-4*1))/2[x²=1,5 +√5/2,x²=1,5-√5/2;[x=±(√5+1)/2,x=±(√5- 1)/2; x⁵-x^-5=(√5+1)⁵/2⁵-(√5+1)^-5/2^-5= (176+80√5)/32-32/(176+80√5)=5,5+2,5 √5-1/(5,5+2,5√5)=5,5+2,5√5-(5,5-2,5√5)/(5,5²-2,5²*5)=11,=-11,=((√5-1)/2)⁵-1/(√5/ 2-1/2)⁵=(80√5-176)/32-32/(80√5-176)= 2,5√5-5,5-2(5√5+11)/4=-11,=11
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|х-3|^(х2-х)=(х-3)²,{х-3≥0,(х-3)^(х²-х-2)=1,х-3=0,{х≥3,х-3=1,х2-х-2=0, {х=3;{х<3,(х-3)^(х²-х-2)(-1)^(х2-х)=1;[{х≥3,х=3,х=4,х=(1±√(1-4*-2))/2,{х<3, х=3,х=4,[х=2, х=-1,х-3=-1,х2-х-2:2;[{х=3,х=4;х=2,х=1,х=2,4-2-2=0:2✓;{3;4;2;1}
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{(cosy-sinx+1)(tg²(x-π/3)+tg²(y+π/6))=0,(sinx-cosy)(2-sin2y+siny)=0;{[cosy=sinx-1;tg(x-π/3)=0,tg(y+π/6)=0,[sinx=cosy,{sin2y=1,siny=-1;{[y=±arccos(sinx-1)+2πr,x-π/3=πl,y+π/6=πp,[x=(π/2-y)(-1)^k+2k,π/2-y≥-π/2,≤π/2 {2y=π/2+2πn,y=-π/2+2πm,{[y=±arccos(sinx-1)+2πr,x=π/3+πl,y=-π/6+πp,[x=π/2-y+2πk,x=π/2+y+2πk,yє[0;π]{у=π/4+πn,y=-π/2+2πm;1+4n=-2+8πm,0/
{[-π/6+πp=±arccos(sin(π/3+πl)-1)+2πr, x=π/3+πl π/3+πl=π/2-y+2πk,yє[0;π],y=-π/6+πp,{-π/6=±arccos(√3/2-1)+π(2r-p), y=-π/6+π(l-2k),x=π/2+y+2πk,yє[0;π];
[{0/, x=π/3+2πk, π/6=y,0/,{0/, y=5π/6,x=8π/6+2πk;{π/3+2πk;π/6}{4π/3+2πk;5π/6}
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1/x(333/ln10-100x¹⁰⁰)=0 x=±(3,33/ln10)⁰,⁰¹°0+*->x max=3,33lg(3,33/ln10/e)=-3,33*0,..>-6,67 x=10^(n/100) 3,33n-10^n?-6,67 n=1;-2 x=10⁰,⁰¹;10-⁰,⁰²
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y'(x)=e^(xy),xy=z,y+xy'=z',y'=z'/x-z/x² z'/x-z/x²=e^z,(e^-z)'+ze^-z/x=-x,-z'/z+1/x =0,-ln|z|+ln|x|=C,z=±x/e^C=cx,z=-1/x,z=cx -1/x,y=c-1/x²
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0-3;3-5 6!/(6-5)!*2=120*6*2=720*2=1440
0,1,2,3,4,5:5!=120 1,2,3,3,4,5:3!*С(5;2)= 6*5!/2!/3!=6*20/2=60 1,2,3,4,5,0:5!=120 300
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$ctg⁷xdx=$-cos⁷x/(1-cos²x)⁴dcosx=$-y⁷/(y²-1)⁴dy=$(A/(y-1)+A1/(y-1)²+A2/(y-1)³ +A3/(y-1)⁴+A4/(y+1)+A5/(y+1)²+A6/(y+ 1)³+A7/(y+1)⁴)dy
A(y⁷+y⁶-3y⁵-3y⁴+3y³+3y²-y-1)+A1(y⁶+2y⁵-y⁴-4y³-y²+2y+1)+A2(y⁵+3y⁴+2y³-2y²-3y-1)+A3(y⁴+4y³+6y²+4y+1)+A4(y⁷-y⁶-3y⁵+3y⁴+3y³-3y²-y+1)+A5(y⁶-2y⁵-y⁴+4y³-y²-2y+1)+A6(y⁵-3y⁴+2y³+2y²-3y+1)+A7(y⁴-4y³+6y²-4y+1)=-y⁷,{A+A4=-1,-A1+2A4-A5=1,1/2A2+2A4- 2A5+1/2A6=-1/2,-1/6A3+1 1/3A4-1,5A6 -1/6A7=1/6,2/3A4+1/3A5-1,5A6-1/3A7=13/24, 1/3A5+2 7/36A6-1/4A7=34/72, 503/180A6-23/60A7=59/360, A7=-7697/5186;
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(|х|-|4-|у||-4)²≤4 {|х|-|4-|у||-4≤2,|х|-|4-|у||-4≥-2;{|х|-|4-|у||≤6,|х|-|4-|у||≥2; {[{х-|4-у|≤6,х≥0,у≥0;{х-|4+у|<6,х≥0,у<0;{-х-|4-у|≤6,х<0,у≥0;{-х-|4+у|≤6,х<0,у<0;[{х-|4-у|≥2,х≥0,у≥0;{х-|4+у|≥2,х≥0,у<0;{-х-|4-у|≥2,х<0,у≥0;{-х-|4+у|≥2,х<0,у<0;{[{4-у≤-6+х,4-у≥6-х,х≥0,у≥0;{4+у≥-6+х,4+у≤6-х,х≥0,у<0;{4-у≥-6-х,4-у≤6+х,х<0,у≥0;{4+у≥-х-6,4+у≤х+6,х<0,у<0;[{4-у≤-2+х,4-у≥2-х,х≥0,у≥0;{4+у≤-2+х,4+у≥2-х,х≥0,у<0;{4-у≤-2-х,4-у≥2+х,х<0,у≥0;{4+у≤-2-х,4+у≥2+х,х<0,у<0;
{[{у≤10-х,у≥-2+х,х≥0,у≥0;{у≥-10+х,у≤2-х,х≥0,у<0;{у≤10+х,у≥-2-х,х<0,у≥0;{у≥-х-10,у≤х+2,х<0,у<0;[{у≥6-х,у≤2+х,х≥0,у≥0;{у≤-6+х,у≥-2-х,х≥0,у<0;{у≥6+х,у≤2-х,х<0,у≥0;{у≤-6-х,у≥-2+х,х<0,у<0;
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1+log√2√(x+4)+log0,5(13-x)/(|x²+2x-3|-|2x²-10x+8|)≥0
{x+4≥0, x+4>0,13-x>0,|x²+2x-3|-|2x²-10x +8|≠0;{x>-4,x<13,|x²+2x-3|≠|2x²-10x+8|;{xє(-4;13),х²+2х-3≠2х²-10х+8,х²+2х-3≠-2х²+10х-8;{xє(-4;13),-х²+12х-11≠0,3х²-8х+ 5≠0;{хє(-4;13),х≠(-12±√(144-4*1*-11))/-2, х≠(8±√(64-4*3*5))/6;{хє(-4;13),х≠1,х≠11, х≠5/3,х≠1;хє(-4;1)U(1;1 2/3)U(1 2/3;11)U (11;13) (1+log2(x+4)-log2(13-x))/(|x²+2x-3|-|2x²-10x+8|)≥0,log(2)(2(x+4)/(13-x))/|(x-1)(x+3)|-2|(x-1)(x-4)|)≥0, -4**1+*1 2/3+*11->x
2*5 2/3/(11 1/3)=10 4/3/(11 1/3)=1 xє(1;1 2/3)U(1 2/3;11)
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{a<3log(3)x,ax≥9,|x-9|+|x-27|≤18; ОДЗ:x>0,{{a<3log(3)x,a≥9,[{x-9+x-27≤18,х≥27,{х-9-х+27≤18,хє[9;27){-х+9-х+27≤18;х<9;{9<3log(3)x,a≥9,[{2x≤54,х≥27,{18≤18,хє[9;27){-2х≤-18;х<9;{3³<x,a≥9,[x=27,[9;27)0/;{а≥9,х>27,хє[9;2 7] 0/
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log(1/7)log3((|-x+1|+|x+1|)/(2x+1))≥0, 0<log3((|-x+1|+|x+1|)/(2x+1))≤1,{(|-x+1|+|x+1|)/(2x+1)≤3,(|-x+1|+|x+1|)/(2x+1)>1; +;-1+;+*1-;+>x [{(x-1+x+1)/(2x+1)≤3,(x-1|x+1)/(2x+1)>1,x≥1,{(-x+1+x+1)/(2x+1)≤3,(-x+1+x+1)/(2x+1)>1,xє[-1;1){(-x+1-x-1)/(2x+1)≤3,(-x+1-x-1)/(2x+1)>1,х<-1;[{2х/2/(x+0,5)-3≤0,2x/2/(x+0,5)-1>0,x≥1,{2/2/(x+1/2)≤3,2/2/(x+0,5)-1>0,xє[-1;1){-2х/(2x+1)-3≤0,-2х/(2x+1)-1>0,х<-1;[{(х-3х-1,5)/(x+0,5)≤0,(x-х-0,5)/(x+0,5)>0,x≥1,{(1-3х-1,5)/(x+1/2)≤0,(1-х-0,5)/(x+0,5)>0,xє[-1;1){(-х-3х-3/2)/(x+0,5)≤0,(-х-х-0,5)/(x+1/2)>0,х<-1;[{(х+0,75)/(x+0,5)≥0,+-°+>х x+0,5<0,x≥1,{(х+1/6)/(x+1/2)≥0,+°*+>х(х-0,5)/(x+0,5)<0,+°-*+>хxє[-1;1){(х+3/8)/(x+0,5)≥0,+°-*+>х,(х+0,25)/(x+1/2)<0,+°-*+>хх<-1;[{хє(-∞;-0,75]U(-0,5;+∞),x<-0,5,x≥1,{xє(-∞;-0,5)U[-1/6;+∞)xє(-0,5;0,5)xє[-1;1){хє(-∞;-0,5)U[-3/8;+∞),xє(-0,5;-0,25),х<-1;[0/,хє[-1/6;0,5),0/, хє[-1/6;+0,5)
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54^х√3^((5х-10)/(х+2))/√(2х+9)≤81*2^х*(2х+9)^-0,5/3^((х-2)/(х+2)),2^х3^(3х)*3^((2,5х-5)/(х+2))/√(2х+9)-81*2^х/√(2х+9)3^(-(х-2)/(х+2))≤0,2^х*3^(-(х-2)/(х+2))(3^(3х+3,5 (х-2)/(х+2))-81)/√(2х+9)≤0, {3^((3х²+6х+3,5х-7)/(х+2))-81≤0,2х+9>0;{(3х²+9,5х-7)/(х+2)≤4, х>-4,5;{(3х²+9,5х-7-4х-8)/(х+2)≤0(1),х>-4,5;(1) (3х²+5,5х-15)/(х+2)≤0,(х-(-5,5+√(5,5²-4*3 15))/6)(х-(-11/12-√(30,25+120 30)/6)/(х+2)≤0,-11/12-√180,25+*2-*-11/12+√180,25/6+>х хє(-∞;-11/12-√180,25/6]U(-2;-11/12+√180,25/6],x>-4,5 xє(-4,5;-11/12-√180,25/6]U (-2;-11/12+√180,25/6]
180,25=13,..2 1/6\2+11/12=2 13/12, 2 1/6\2-11/12=1 3/12
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[х+1/2]=1/2х⁶-[х] 1/2х⁶єZ x:2,x=2n [2n+1/2]=1/2(2n)⁶-[2n] 2n-32n⁶+2n=0, 32n(n⁵-1/8)=0, n=0, n=1/8^(0,2) {x}є[0;0,5) 2[х]-0,5х⁶=0,≤2х-0,5х⁶,>2(х-1)-0, 5х⁶ {-0,5х(х⁵-4)≥0,*+*4⁰,²->х-0,5х⁶-2х-2<0;{хє(-∞;0]U[4⁰,²;+∞),x⁶+4x+4>0;{хє(-∞;0]U[4⁰,²;+∞),xєR, xє[m;m+0,5)U[4⁰,²;1,5)U[m;m+0,5),х=4^(1/6)
6х⁵+4=0,х=(-4/6)^(1/5)=-(2/3)⁰,² 2/3(2/3) ⁰,²-4*(2/3)⁰,²+4=-3 1/3(2/3)⁰,²+4>0
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1+2^х+2^(2х+1)=у², х,уєZ [у>1, у<-1; (1+2^х*0,5)²+2^(2х)*1,75=у², х<0, ((2^(-х)+0,5)²+1,75)/2^(-2х)\>1, при х=0, 4=у², у=±2, ((2^(-х)+0,5)²+1,75)/2^(-2х) будет равняться (1;4), а на этом промежутке квадратов целых чисел нет. х=1, 1+2+ 2³=11, у=+√11, х=2, 1+2²+2⁵=5+32=37, у= ±√37, х=3, 1+2³+2⁷=9+128=137, у=±√137, 1+2^х+2^(2х+1)-1-2^х1-2^(2х1+1)=у²-у1²>0, 2^х1(2^(х-х1)+2^(2х+1-х1)-1-2^(х1+1)) =(у-у1)(у+у1),:/2,:4, х1≥2, потому что скобка не кратна 2, а значит взаимно проста со степенью, НОД(у1,(у-у1)/2)=1, иначе решений нет. 1+2+8=11 равноостаточно с простым числом, а квадрат целого числа не может давать остаток как у 11 при делении на простое число:11:3=3(ост.2)х=3, 0^2=0,1²=1,2²==1, короче говоря, при х>0 решений нет.
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(√x+x^-0,25)⁹=x⁴,⁵+9√x⁸x^-0,25+9!/2!/7!√x⁷x^-0,5+9!/3!/6!√x⁶x^-0,75+9!/4!/5!√x⁵x^-1+9!/5!/4!√x⁴x^-1,25+9!/6!/3!√x³x^- 1,5+9!/7!/2!√x²x^-1,75+9√xx^-2+x^-2,25 =x⁴,⁵+9x^3,75+36x^3+84x^2,25+126x¹,⁵+126x^0,75+84+36x^-0,75+9x^-1,5+x^-2,25
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X¹/²+y¹/²=1 y=(1-√x)² $(0;1)(1-2√x+ x)dx=x-2x¹,⁵/1,5+x²/2(0;1)=1/6 L=$(0;1)2√2√(0,25+(x⁰,⁵-0,5)²)dx⁰,⁵= 2√2(0,5(x⁰,⁵-0,5)√(0,25+(x⁰,⁵-0,5)²)+ 0,125ln|x⁰,⁵-0,5+√((x⁰,⁵-0,5)²+0,25)|)(0;1)=1+0,5√2ln(√2+1)
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log(2)²(ax)+log²(2)((1-a)/x) x наименьшее, а максимально {ax>0,(1-a)/x>0;[{a≥1,x>0,x<0;{aє[0;1) х>0,х>0;{а<0,х<0,х>0;[0/,ає[0;1)х>0,0/;[ає[0;1)х>0 2log(2)(ax)*1/(ax)*a+2log(2)((1-a)/x)*1/((1-a)/x)*(1-a)*-x^(-2)=2log(2)(ax)/x-2l og(2)((1-a)/x)x^-1=0, log(2)(ax/((1-a)/x)) =0,ax/(1-a)*x=1, x²=(1-a)/a, x=±√((1-a)/a) -+>x min log(2)²(a√((1-a)/a))+log²(2)((1-a)/√((1-a)/a))=0,25log(2)²((1-a)a) +0,25log(2)²((1-a)a)=0,5log(2)²((1-a)a) 0,5*2log(2)(a-a²)*1/(a-a²)*(1-2a)=0, [log(2)(a-a²)=0,1-2a=0; [a-a²=1,a=1/2; -a²+a-1=0,a=(-1±√(1-4-1*-1))/-2[a=0,5±√-3/2 0/, +*->a {0,5}
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arcsincosx=cosarcsin(x-a)≤π/2,-π/2 arcsinsin(π/2-x)=sin(π/2-arcsin(x-a)) [{π/2-x=√(1-(x-a)²),π/2-x≤π/2,≥-π/2,arcsin(x a)є[-π/2+2πn;π/2+2πn];{π/2-x=-√(1-(x-a)²),π/2-x≤π/2,≥-π/2,arcsin(x -a)є[π/2+2πn;3π/2+2πn];{π-(π/2-x)=√(1-(x-a)²),π/2-x≥π/2,≤π,arcsin(x -a)є[-π/2+2πn;π/2+2πn];{π/2+x=-√(1-(x-a)²),π/2-x≥π/2,≤π,arcsin(x -a)є[π/2+2πn;3π/2+2πn];[{π²/4-πx+x²=1-(x-a)²,x≥0,≤π,arcsin(x-a)є[-π/2;π/2];{π²/4-πx+x²=1-(x-a)²,x≥0,≤π,arcsin(x-a)=π/2;{(π/2+x)²=1-(x-a)²,x≤0,≤-π/2,arcsin(x -a)є[-π/2;π/2];{(π/2+x)²=1-(x-a)²,x≤0,≥-π/2,arcsin(x-a)=π/2;[{x=(π+2a±√(π²+4aπ+4a²-2π²+8-8a²))/4π²/4,x≥0,≤π,x-aє[-1;1];{x=(π+2a±√((π+2a)²-4*2(π²/4-1+a²)))/4,x≥0,≤π,x-a=1;{x=(-π+2a±√((π-2a)²-4*2(π²/4-1-a²)))/4,x≤-π/2,x -aє[-1;1];{(π/2+x)²=0,x≤0,≥-π/2,x-a=1;[{x=0,25π+0,5a±√(-(π-2a)²+8)/4,x≥0,≤π,xє[a-1;a+1];{a+1=π/4+0,5a±√(-π²+4πa-4a²+8)/4,x≥0,≤π,x=a+1;{x=-π/4+0,5a±√(-π²-4πa+8+12a²)/4,x≤-π/2,xє[a-1;a+1];{x=-π/2,x≤0,≥-π/2,x=a+1;[{x=0,25π+0,5a±√(-(π-2a)²+8)/4,π-2a≤√8,π-2a≥-√8;aє[-1;1+π],xє[0;π]xє[a-1;a+1];{(0,5a+1-π/4)²=(-π²+4πa-4a²+8)/16,x≥0,≤π,x=a+1;{x=-π/4+0,5a±√(-π²-4πa+8+12a²)/4,(a-(4π+√(16π²-4*12(-π²+8)))/24)(a-(π/6-√(16π²+48π²-364)/4)≥0,+**+>а a≤1-π/2,x≤-π/2,xє[a-1;a+1];{x=-π/2,a=-π/2-1;
{x=0,25π+0,5a±√(-(π-2a)²+8)/4,a≥0,5π-√2,a≤0,5π+√2,aє[-1;1+π],xє[0;π]xє[a-1;a+1];ає[0,5π-√2;0,5π+√2]ає[0,339;0,512] хє[1,339]
[ає[0,339;0,512] хє[1,339],ає[π/6-√(4π²-22,75);1-π/2]x=-π/4+0,5a±√(-π²-4πa+8+12a²)/4,x≤-π/2,xє[a-1;a+1],а⁴-2πа³-(-1,5π²+4,25)а²+-(2+0,5π³-4,5π)а-17/16π²+π/2+π⁴/16+3=0, ає[-1;π-1]x≥0,≤π,x=a+1;х=-π/2,а=-π/2-1;[ає[π/6-√(4π²-22,75);1-π/2]U{-π/2-1}U[0,339;0,512],{a=2,26..,a=0,06,a=0,33,a =3,62>2,14.. aє[-1;π-1] ає[π/6-√(4π²-22,75);1-π/2]U{0,06}U{0,33}U[0,339;0,512],
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x²-290x=289√x x⁰,⁵(x¹,⁵-290x⁰,⁵-289)=0[x= 0,x⁰,⁵=(289/2+√(144,5²+(-290)³/27))^(1/3) +(289/2-√(-71'493'289,75)/9)^(1/3)=2√(2 90/3)cos(1/3arccos(867/168200√870)+ 2πn/3);✓,-..,-.. [x=0,x=1160/3cos²(1/3arcc os(867/168200√870)).[√(x-x⁰,⁵)=0,√(x-x⁰,⁵) =√(1160/3cos²(1/3arccos(867/168200√ 870))-2√(290/3)cos(1/3arccos(867/1682 00√870)))=18 2/3...16,.. .
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231<(2n+m-1)/2*m<245,{0,5m²+(n-1/2) m-231>0,0,5m²+(n-1/2)m-245<0; {(m-(-n+ 1/2+√((n-1/2)²-4*0,5*231))/1)(m-(-n-√(n² -n+1/4+462)))>0+**+>m,(m-(-n+1/2+√((n-1/2)²-4 *0,5(-245)))/1)(m-(-n-√(n²-n+1/4+490)))<0;+°-°+>m {mє(-∞;-n+1/2-√(n²-n+462,25))U(-n+1/2+√(n²-n+462,25);+∞),mє(-n+1/2-√(n²-n+49 0,25);-n+1/2+√(n²-n+490,25)) mє(-n+1/2-√(n²-n+490,25);-n+1/2-√(n²-n+460,25))U(-n+1/2+√(n²-n+460,25);-n+1/2+√(n²-n+490,25)) 1/2+√460,25=1/2+21,9 2=22,42 1/2+22 6,25/44=22 28,25/44=2 2,6.. поэтому промежуток с ростом n будет уменьшаться и не останется ни одного целого числа.
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{|х-4|+3|у|=2,9у²+х²-8х+4(а+3)=0;{[{х-4+3у=2,х-4≥0,у≥0,{х-4-3у=2,х≥4,у<0,{-х+4+3у=2,х<4,у≥0,{-х+4-3у=2,х<4,у<0;(х-4)²+(3у)²=-4а+4;≥0 {[{у=2-х/3,х≥4,у≥0,{у=-2+1/3х,х≥4,у<0,{у=х/3-2/3,х<4,у≥0,{у=-1/3х+2/3,х<4,у<0;(х-4)²+(3у)²=-4а+ 4;а≤1 x≤6,y≤2/3 (6-4)²+(2/3-0)²=4+4/9=r², r=2√10/3 2√10≤-4a+4,a≤-0,5√10+1,R=2, 2≥-4a+4,a≥0,5, aє[0,5;-0,5√10+1]
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f(x)=10^(x/50)-4*10^(x/100)-3*10 ^(-x/100)+12*10^(-x/50) f'(x)=ln10(10^(x/25)+2*10^(3x/100)+1,5*10^(x/100)-12)*10^(-x/50)/50=0 (10^(x/100)+0,5)⁴-1,5 (10^(x/100)+0,5)²+2,5(10^(x/100) +0,5)-12 15/16=0 (z-0,25)³+51/16(z-0,25)+183/256=0 z=0,25+(-183+√357'921)¹/³/8+(.. ..)..;0,25-(-183+√357'921)¹/³/16-(.. -..)..±√(3/4((-183+√357'921)¹/³/8+(..-..)..)²+51/16)i x=100lg(-0,5-√(0, 25+(-183+√357'921)¹/³/8+(.. -..)..)+2√(0,5√(13/4-0,25((-183+√357'92 1)¹/³/8+(..-..)..)+((-183+√357'921)¹/³/8+(..-..)..)²)+1/8-(-183+√357'921) ¹/³/32-(..-..)..))*+>x min=(-0,5-√(0, 25+(-183+√357'921)¹/³/8+(.. -..)..)+2√(0,5√(13/4-0,25((-183+√357'92 1)¹/³/8+(..-..)..)+((-183+√357'921)¹/³/8+(..-..)..)²)+1/8-(-183+√357'921) ¹/³/32-(..-..)..))²-4*(-0,5-√(0,25+(-183 +√357'921)¹/³/8+(.. -..)..)+2√(0,5√(1 3/4-0,25((-183+√357'92 1)¹/³/8+(.. -..)..)+((-183+√357'921)¹/³/8+(.. -..)..)²)+1/8-(-183+√357'921)¹/³/32- (..-..)..)-3/(-0,5-√(0,25+(-183+√357'9 21)¹/³/8+(.. -..)..)+2√(0,5√(13/4-0,2 5((-183+√357'921)¹/³/8+(..-..)..)+((- 183+√357'921)¹/³/8+(..-..)..)²)+1/8- (-183+√357'921)¹/³/32-(..-..)..)+12/ (-0,5-√(0, 25+(-183+√357'921)¹/³/8 +(.. -..)..)+2√(0,5√(13/4-0,25((-183+ √357'92 1)¹/³/8+(..-..)..)+((-183+√3 57'921)¹/³/8+(..-..)..)²)+1/8-(-183+√ 357'921)¹/³/32-(..-..)..))² 0/
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3х²-4|х²-1|+х-1=0,[{х²-1≥0,-х²+х+3=0;{х²-1<0,7х²+х-5=0;[{(х-1)(х+1)≥0+*+>х, х=(-1±√(1 -4-1*3))/-2;{(х-1)(х+1)<0+ **+>х,х=(-1±√(1-4*7 *-5))/14;[{хє(-∞;-1]U [1;∞),[x=1/2-0,5√13,x=0,5+0,5√13;{хє(& 1;1),[х=-1/14+√141/14,х=-1/14-√141/14;[х=0,5-0,5√13,х=0,5+0,5√13,х=-1/14+√141/14,х=-1/14-√141/14.
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2/log(2)(2x-2)+3/log(2)(4x-4)≤8/(log(3) 27+log(2)(x-1)),{2x-2>0,4x-4>0,x-1>0;{x>1,x>1,x>1;хє(1;+∞) 2/(log(2)(x-1)+1)+ 3/(log(2)(x-1)+2)-8/(3+log(2)(x-1))≤0, (2(log(2)(x-1)+2)(log(2)(x-1)+3)+3(log(2)(x-1)+1)(log(2)(x-1)+3)-8(log(2)(x-1)+1)(log(2)(x-1)+2))/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log(2)(x-1)+3)≤0,(2log²(2)(x-1)+10log(2)(x-1)+12+3log²(2)(x-1)+12 log(2)(x-1)+9-8log²(2)(x-1)-24log(2)(x-1)-16)/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log(2)(x-1)+3)≤0,(-3log²(x-1)-2log(2)(x-1) +5)/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log (2)(x-1)+3)≤0,(log(2)(x-1)-(2+√(4-4*3* 5))/-6)(log(2)(x-1)-(-1/3+√64/6))/(log(2)(x-1)+1)/(log(2)(x-1)+2)/(log(2)(x-1)+3)≥ 0,-°-3+°-2*-1 2/3+°-1-1*+>log(2)(x-1) log(2)(x-1)є(-3;-2)U[-1 2/3;-1)U[1;+∞) [x-1 >1/8,x-1<1/4;x-1≥1/2/4^(1/3),x-1≤1/2;x-1≥2;[x>1 1/8,x<1 1/4,x≥1+2^(-1 2/3),x≤1,5, x≥3;хє(1 1/8;1 1/4)U[1+2^(-1 2/3);1,5]U [3;+∞)
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x->'=(3 -1;-1 3)x->+(4;4)e^2t x->(0)=(1 1) x->0'=(3 -1;-1 3)x-> (A-лI)x->0=0,|3-л -1;-1 3-л|=0,(3-л)²-(-1)²=0,[3-л=1,3-л=-1;[л=2,л= 4;(1 -1;-1 1)*(a b)=0,{a-b=0,-a+b=0;{a=b,a= b;(1;1)(-1 -1;-1 -1)(a b)=0,{-a-b=0,...;a=-b (1;-1) х->0=С1(1;1)е^2t+C2(1;-1)e^4t x-> p=(A;B)e^2t,2(A;B)e^2t=(3 -1;-1 3)(A B)e ^2t+(4;4)e^2t,(2A;2B)=(3A-B+4;-A+3B+4) {2A=3A-B+4,2B=-A+3B+4;{-A-B=4,A-B=4;{A=0,B=-4; xp->=(0;-4)e^2t x->=С1(1;1)е^ 2t+C2(1;-1)e^4t+(0;-4)e^2t (1 1)=C1(1;1) +C2(1;-1)+(0;-4)=(C1+C2;C1-C2-4){C1+ C2=1,C1-C2-4=1;{C1+C2=0,C1-C2=5;{C1=2,5,C2=-2,5; x->=(2,5;-1,5)e^2t+(-2,5; 2,5)e^4t
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4x=|3x-|x+a||+9|x-3|≥0,x≥0[{x≥a/2,x≥-a,x≥ 3;a/7+27/7=x;{x≥a/2, x≥-a,x<3,x=-a/11+ 27/11;{x≥-a/4,x<-a,x≥3, a/7-27/7=x;{x≥-a/4,x<-a,x<3,x=a/9+3;{x<a/2,x≥-a,x≥3,-a/3+9 =x;{a>54/13,a<18,x=a/15+9/5;{a<-108/5, a≥-24,a+27=x;{a<-8 4/13,a>-24,x=-a/17+2 7/17;
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(373,15К;101325Па)(647,3К;22,1МПа)(273,16К;610Па) P=aT²+bT+c {a*373,15²+ 373,15b+c=101325,373,15b+1,576c=(101325-22,1*576²)/0,424, -0,79c=(101325-22, 1*576²)/0,424+(101325-610*1,3660²)/0,3 66;
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x²+4xy+y²+1/4=0, x=(-4y±√(16y²-4*(y²+ 1/4)))/2=-2y±√(16y²-4y²-1)/2=-2y±√(12y²- 1)/2,12y²-1≥0,(y-1/√12)(y+1/√12)≥0, +**+>y,yє(-∞;-1/√12]U[1/√12;+∞) √(1-4(-2y±√(3y²-1/4))²)-√(1-4y²)-2x -2y=0,√(2-28y²±16y√(3y²-1/4))-√(1-4y²)+2y-+2√(3y²-1/4)=0,2-28y²±16y√(3y²-1/4)-2√(2-28y²±16y√(3y²-1/4))√(1-4y²)+1-4y²=4y²±8y√(3y²-1/4)+4(3y²-1/4),±8y√(3y²-1/4)+4-48y²-2√(2-28y²±16y√(3y²-1/4)√(1-4y²)=0,64y²(3y²-1/4)±16y√(3y²-1/4)(4-48y²)+(4-48y²)²=4(2-28y²±16y√(3y ²-1/4)) 2496y⁴-288y²+8=±768y³√(3y²-1/ 4) 2496²y⁸+288²y⁴+8²-2*2496*288y⁶+ 2*2496*8y⁴-2*288*8y²=768²y⁶(3y²-1/4), (312²-96²*3)y⁸+(-624*36+96²/4)y⁶+(1296 +624)y⁴-72y²+1=0,y²=a,≥0,aє[1/12;1/4]144*(26²-64*3)a⁴+144(-52*3+16)a³+1920a²-72a+1=0,144*16*157a⁴-144*140a³+1920a²-72a+1=0, (а²-35/8/157а+0,00226..)² 7,28*10^-5а-4,29*10^-6=0,\>/> минимум а=35/8/157/2=35/16/157,-1,01*10^-6<0 поэтому есть 2 корня, а=0,014,а=0,010 у=±0,12..>0,289,<-0,289,у=±0,101>0,288,<-0,289 0/
169-12=157
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{logx+(logx+8logy)/(log²x+log²y)=2,logy+ (8logx-logy)/(log²x+log²y)=0;{log³x+logx log²y+logx+8logy=2log²x+2log²y,log²xlogy-log³y+8logx-logy=0;{log²y(logx-2)+8logy +log³x-2log²x+logx=0,log²xlogy-log³y+8logx-logy=0;{logy=(-8±√(64-4(logx-2)(log³x 2log²x+logx)))/2/(logx-2),[log²x(-8+√(-4lo g⁴x+16log³x-20log²x+8logx+64)/(2logx-4) -(-8+√(-4log⁴x+16log³x-20log²x+8logx+64)³/(2logx-4)³+8logx-(-8+√(-4log⁴x+16log³ x-20log²x+8logx+64)/(2logx-4)=0; log²x(-8-√(-4log⁴x+16log³x-20log²x+8logx+64)/(2logx-4)-(-8-√(-4log⁴x+16log³x-20lo g²x+8logx+64)/(2logx-4)+8logx-(-8-√(-4lo g⁴x+16log³x-20log²x+8logx+64)/(2logx-4) =0;(log²x-2logx+1/2)²-16,25≤0,(log²x-2lo gx-√16,25+0,5)(log²x-2logx+0,5+√16,25) ≤0,(logx-(2+√(4-4(-√16,25+0,5)))/2)(logx (2-√(4√16,25+2))/2)≤0,+*-*+>logx logxє [1-√(√16,25+0,5);1+√(√16,25+0,5)],[logx=0,logx=1,logx=2,logx=3,12,logxє [1-√(√16,25+0,5);1+√(√16,25+0,5)];[logx=0,=1,=2,=3,12;[x=1,x=10,x=100,x=1 0³,¹²;[y=1,y=10000;y=1,y=10⁸,y=10^(-1/4), y=10^(-25/7+√81678,7456/224),y=10^(-25/7-√81678,224).
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