Question

Не вычисляя корней уравнения 3x^2+8x-1=0 найдите x1^2+x2^2​

Answer 1

$7\frac{7}{9}$

Объяснение:

$3x^{2}+8x-1=0 \quad | \quad :3$

$x^{2}+\frac{8}{3}x-\frac{1}{3}=0;$

$\left \{ {{x_{1}+x_{2}=-\frac{8}{3}} \atop {x_{1} \cdot x_{2}=-\frac{1}{3}}} \right. ;$

$x_{1}+x_{2}=-\frac{8}{3};$

$(x_{1}+x_{2})^{2}=(-\frac{8}{3})^{2};$

$x_{1}^{2}+2x_{1}x_{2}+x_{2}^{2}=\frac{64}{9};$

$x_{1}^{2}+x_{2}^{2}=\frac{64}{9}-2x_{1}x_{2};$

$x_{1}^{2}+x_{2}^{2}=\frac{64}{9}-2 \cdot (-\frac{1}{3});$

$x_{1}^{2}+x_{2}^{2}=\frac{64}{9}+\frac{2}{3};$

$x_{1}^{2}+x_{2}^{2}=\frac{64}{9}+\frac{6}{9};$

$x_{1}^{2}+x_{2}^{2}=\frac{70}{9};$

$x_{1}^{2}+x_{2}^{2}=7\frac{7}{9};$