Question

07 Considere a equação x2 +3x - 10 = 0 e
sejam X1 e X2 suas raízes. Então, (x1)2 + (x2)? vale:
(A) 2
(B) -5
(C) 29
(D) 30​

Answer 1

• Completando quadrados:

x² + 3x - 10 = 0

x² + 3x = 10

x² + 3x + 9/4 = 10 + 9/4

(x + 3/2)² = 49/4

(x + 3/2)² = (7/2)²

x + 3/2 = ± 7/2

x = (- 3 ± 7)/2

x2 = (- 3 + 7)/2

x2 = 4/2

x2 = 2

2(x1) + (x2) = 2(- 7/2) + 2

2(x1) + (x2) = - 7 + 2

2(x1) + (x2) = - 5

(x1)² + (x2)² = 2² + (- 5)²

(x1)² + (x2)² = 4 + 25

(x1)² + (x2)² = 29

Resposta: (C) 29

Answer 2

Explicação passo-a-passo:

$\sf x^2+3x-10=0$

$\sf \Delta=3^2-4\cdot1\cdot(-10)$

$\sf \Delta=9+40$

$\sf \Delta=49$

$\sf x=\dfrac{-3\pm\sqrt{49}}{2\cdot1}=\dfrac{-3\pm7}{2}$

$\sf x_1=\dfrac{-3+7}{2}~\Rightarrow~x_1=\dfrac{4}{2}~\Rightarrow~\red{x_1=2}$

$\sf x_2=\dfrac{-3-7}{2}~\Rightarrow~x_2=\dfrac{-10}{2}~\Rightarrow~\red{x_2=-5}$

Assim:

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

$\sf (x_1)^2+(x_2)^2=4+25$

$\sf \red{(x_1)^2+(x_2)^2=29}$

Letra C