Question

Найдите сумму квадратов корней уравнения

Answer 1

4x² - 9x - 1 = 0

По теореме Виета :

$x_{1}*x_{2}=-\frac{1}{4}\\\\x_{1}+x_{2}=\frac{9}{4}\\\\(x_{1}+x_{2})^{2} =(\frac{9}{4})^{2}\\\\x_{1}^{2}+2*x_{1}*x_{2}+x_{2}^{2}=\frac{81}{16}\\\\x_{1}^{2}+2*(-\frac{1}{4})+x_{2}^{2}=\frac{81}{16}\\\\x_{1}^{2}-\frac{1}{2}+x_{2}^{2}=\frac{81}{16}\\\\x_{1}^{2}+x_{2}^{2}=\frac{81}{16}+\frac{1}{2}\\\\x_{1}^{2}+x_{2}^{2}=\frac{89}{16}\\\\x_{1}^{2}+x_{2}^{2}=5\frac{9}{16}\\\\Otvet:\boxed{5\frac{9}{16}}$