Question

2 – Considere a equação x2 - 4x – 5 = 0 e sejam x1 e x2 suas raízes. Então quanto vale (x1)2 + (x2)2?

Answer 1

Explicação passo-a-passo:

$\sf x^2-4x-5=0$

$\sf \Delta=(-4)^2-4\cdot1\cdot(-5)$

$\sf \Delta=16+20$

$\sf \Delta=36$

$\sf x=\dfrac{-(-4)\pm\sqrt{36}}{2\cdot1}=\dfrac{4\pm6}{2}$

$\sf x_1=\dfrac{4+6}{2}~\rightarrow~x_1=\dfrac{10}{2}~\rightarrow~x_1=5$

$\sf x_2=\dfrac{4-6}{2}~\rightarrow~x_2=\dfrac{-2}{2}~\rightarrow~x_2=-1$

Logo:

$\sf (x_1)^2+(x_2)^2=5^2+(-1)^2$

$\sf (x_1)^2+(x_2)^2=25+1$

$\sf (x_1)^2+(x_2)^2=26$