Question

найдите сумму квадратов корней уравнения x^{2} + 12х +30=0

Answer 1

x² + 12x + 30 = 0
$D_{1}= (0,5b)^{2}-ac=36-30=6$
$\left \{ {{ x_{1} = \frac{-0,5b+\sqrt{D_{1}}}{a}\atop{x_{2}=\frac{-0,5b-\sqrt{D_{1}}}{a}} \right.$
$\left \{ {{ x_{1}=-6+ \sqrt{6} } \atop {x_{2}=-6-\sqrt{6}}} \right.$
$x_{1} ^{2} + x_{2} ^{2} = (-6-\sqrt{6} )^{2} + (-6+\sqrt{6} )^{2}=$$36- 12\sqrt{6} + 6 + 36+12 \sqrt{6} +6=84$