(3а-4b)x+7z(3a-4b)=(3a-4b)(x+7z)
1) х+у-(х+3у)=7+5
4у=12
у=3
х+3=7
х=4
2) 4х-у-(х+у)=3-6
3х=-3
х=-3
-3-у=6
у=6+3
у=9
3)у-х-(7у+х)=9+3
-6у=12
у=-2
-2-х=9
х=9+2
х=-11
5х+у-х+у=6+10
4х=16
х=4
4+у=-10
у=-10-4
у=-14
Выясним взаимосвязь x+1/x и x²+1/x²
![(x+ \dfrac{1}{x})^2=x^2+ \dfrac{1}{x^2}+2](https://tex.z-dn.net/?f=%28x%2B+%5Cdfrac%7B1%7D%7Bx%7D%29%5E2%3Dx%5E2%2B+%5Cdfrac%7B1%7D%7Bx%5E2%7D%2B2++)
Замена:
![x+ \dfrac{1}{x}=t](https://tex.z-dn.net/?f=x%2B+%5Cdfrac%7B1%7D%7Bx%7D%3Dt+)
![7t-2(t^2-2)=9 \\ -2t^2+7t-5=0 \\ 2t^2-7t+5=0 \\ t_1+t_2= 3,5 \cup t_1t_2=2,5 \\ t_1=2,5 \cup t_2=1](https://tex.z-dn.net/?f=7t-2%28t%5E2-2%29%3D9+%5C%5C+-2t%5E2%2B7t-5%3D0+%5C%5C+2t%5E2-7t%2B5%3D0+%5C%5C+t_1%2Bt_2%3D+3%2C5+%5Ccup+t_1t_2%3D2%2C5+%5C%5C+t_1%3D2%2C5+%5Ccup+t_2%3D1)
Обратная замена
![1) \\ x+ \dfrac{1}{x}=1 \\ x^2-x+1=0 \\ D=1-4\ \textless \ 0](https://tex.z-dn.net/?f=1%29+%5C%5C+x%2B+%5Cdfrac%7B1%7D%7Bx%7D%3D1+%5C%5C+x%5E2-x%2B1%3D0+%5C%5C+D%3D1-4%5C+%5Ctextless+%5C+0+)
нет решений
![2) \\ x+\dfrac{1}{x}=2,5 \\ 2x^2-5x+2=0 \\ x_1+x_2=2,5 \cup x_1x_2=1 \\ x_1=0,5 \cup x_2=2](https://tex.z-dn.net/?f=2%29+%5C%5C++x%2B%5Cdfrac%7B1%7D%7Bx%7D%3D2%2C5+%5C%5C+2x%5E2-5x%2B2%3D0+%5C%5C+x_1%2Bx_2%3D2%2C5+%5Ccup+x_1x_2%3D1+%5C%5C+x_1%3D0%2C5+%5Ccup+x_2%3D2)
Ответ: 0,5; 2