Question

Найти сумму квадратов корней уравнения 2х^2-5х+1=0

Answer 1

$2x^2-5x+1=0 \\ x^2- \frac{5}{2}x + \frac{1}{2} = 0 \\ \left \{ {{x_1 \cdot x_2= \frac{1}{2} } \atop {x_1+x_2= \frac{5}{2} }} \right. \left \{ {{x_1 \cdot x_2= \frac{1}{2}} \atop {(x_1 + x_2)^2 = (\frac{5}{2})^2}} \right. \left \{ {{x_1 \cdot x_2= \frac{1}{2} } \atop {x_1^2+2x_1x_2+x_2^2= \frac{25}{4} }} \right. \left \{ {{x_1 \cdot x_2= \frac{1}{2} } \atop {x_1^2+2 \cdot \frac{1}{2} + x_2^2= \frac{25}{4} }} \right.$
$\left \{ {{x_1 \cdot x_2= \frac{1}{2} } \atop {x_1^2+ x_2^2= \frac{25}{4} - 1 }} \right. \left \{ {{x_1 \cdot x_2= \frac{1}{2}} \atop {x_1^2+x_2^2= \frac{21}{4} }} \right.$
ответ: $\frac{21}{4}$