1).
{3x-2y=5 |*3
{11x+3y=39 |*2
{9x-6y=15
{22x+6y=78
9x-6y+22x+6y=15+78
31x=93
x=3
2y=9-5=4
y=2
Ответ: (3;2)
2).
{5x-4y=8
{15x-12y=18 |:(-3)
{5x-4y=8 (1)
{-5x+4y=-6 (2)
(1)+(2)=>
5x-4y-5x+4y=8-6
0 не равно 2 =>
Решений нет.
B1-b3=12; q=-1/2.
b1-b1*q²=12;
b1(1-q²)=12;
b1(1-1/4)=12;
b1*3/4=12;
b1=12*4/3=16;
S(5)=b1(1-q^5)/(1-q)=16*(1+1/32)/(1+1/2)=16*33/32*2/3=11.
Ответ: 11.
У=1-2х
5х+2(1-2х)=0
5х+2-4х=0
х=-2
у=1-2х=1-2(-2)=1+4
у=5
Ответ: (-2;5)
(а²-1)² = а^4 - 2а^2 + 1
(0,2х-10у)² = 0,04х^2 - 4ху + 100у^2
1 ; x² ; 6 - x²
С одной стороны :
![q=\frac{x^{2} }{1}=x^{2}](https://tex.z-dn.net/?f=q%3D%5Cfrac%7Bx%5E%7B2%7D%20%7D%7B1%7D%3Dx%5E%7B2%7D)
С другой стороны :
![q=\frac{6-x^{2} }{x^{2} }](https://tex.z-dn.net/?f=q%3D%5Cfrac%7B6-x%5E%7B2%7D%20%7D%7Bx%5E%7B2%7D%20%7D)
Приравняем правые части :
![x^{2}=\frac{6-x^{2} }{x^{2} },x^{2}> 0\\\\x^{4}=6-x^{2}\\\\x^{4}+x^{2}-6=0\\\\(x^{2}+3)(x^{2}-2)=0\\\\1)x^{2} -2=0\\x^{2}=2\\\\x_{1}=-\sqrt{2} \\\\x_{2}=\sqrt{2} \\\\2)x^{2}+3=0\\\\x^{2}=-3<0](https://tex.z-dn.net/?f=x%5E%7B2%7D%3D%5Cfrac%7B6-x%5E%7B2%7D%20%7D%7Bx%5E%7B2%7D%20%7D%2Cx%5E%7B2%7D%3E%200%5C%5C%5C%5Cx%5E%7B4%7D%3D6-x%5E%7B2%7D%5C%5C%5C%5Cx%5E%7B4%7D%2Bx%5E%7B2%7D-6%3D0%5C%5C%5C%5C%28x%5E%7B2%7D%2B3%29%28x%5E%7B2%7D-2%29%3D0%5C%5C%5C%5C1%29x%5E%7B2%7D%20-2%3D0%5C%5Cx%5E%7B2%7D%3D2%5C%5C%5C%5Cx_%7B1%7D%3D-%5Csqrt%7B2%7D%20%5C%5C%5C%5Cx_%7B2%7D%3D%5Csqrt%7B2%7D%20%5C%5C%5C%5C2%29x%5E%7B2%7D%2B3%3D0%5C%5C%5C%5Cx%5E%7B2%7D%3D-3%3C0)
решений нет
Ответ : при x = - √2 и x = √2