Question

(×+1)ao quadrado=×+7​

Answer 1

Explicação passo-a-passo:

1°Uso dos produtos notáveis

$(a+b)^{2} = a^{2} + 2ab + b^{2}\\\\\\(x+1)^{2} = x+7\\\\x^{2} + 2x*1 + 1^{2}  = x + 7\\\\x^2 + 2x + 1 = x + 7\\\\x^2 + 2x + 1 -x = 7\\\\x^2 + 2x - x = 7 - 1\\\\x^2 + x = 6\\\\x^2 + x - 6 = 0$

2°Preparando para resolução com fórmula de bhaskara

a = 1

b = 1

c = -6

$x = \frac{-b\ \pm \sqrt{b^{2} - 4*a*c} }{2*a}$

$x_1 = \frac{-1+\sqrt{1^{2} - 4*1*(-6)} }{2*1}\\\\x_1 = \frac{-1+\sqrt{1 - 4*(-6)} }{2}\\\\x_1 = \frac{-1+\sqrt{1 + 24} }{2}\\\\x_1 = \frac{-1+\sqrt{25} }{2}\\\\x_1 = \frac{-1+5 }{2}\\\\x_1 = \frac{4 }{2}\\\\x_1 = 2\\\\\\x_2= \frac{-1-\sqrt{1^{2} - 4*1*(-6)} }{2*1}\\\\x_2= \frac{-1-\sqrt{1 - 4*(-6)} }{2}\\\\x_2= \frac{-1-\sqrt{1 + 24} }{2}\\\\x_2= \frac{-1-\sqrt{25} }{2}\\\\x_2= \frac{-1-5 }{2}\\\\x_2= \frac{-6 }{2}\\\\x_2 = -3$

Answer 2

(x + 1)² = x + 7

(x + 1) • (x + 1)= x + 7

x² + x + x + 1 = x + 7

x² + 2x - x + 1 - 7 = 0

x² + x - 6 = 0

A= 1

B= 1

C= - 6

∆= b² - 4ac

∆= 1² - 4 • 1 • ( - 6)

∆= 1 + 24

∆= 25

x= - b ± √∆ / 2a

x= - 1 ± √25 / 2 • 1

x'= - 1 + 5/2 = 4/2 = 2

x''= - 1 - 5/2 = - 6/2 = - 3

S= ( - 3 , 2)