Question

RESOLVA AS SEGUINTES EQUAÇÕES DO 2° GRAU, EM IR:
(x+1)²=x+7

Answer 1

$\large\begin{array}{l}(x+1)^2=x+7\\\\ x^2+2x+1=x+7\\\\ x^2+2x+1-x-7=0\\\\ x^2+2x-x+1-7=0\\\\ x^2+x-6=0~\Rightarrow~\left\{\! \begin{array}{l}a=1\\b=1\\c=-6 \end{array} \right. \end{array}$


$\large\begin{array}{l} \Delta=b^2-4ac\\\\ \Delta=1^2-4\cdot 1\cdot (-6)\\\\ \Delta=1+24\\\\ \Delta=25 \end{array}$


$\large\begin{array}{l} x=\dfrac{-b\pm \sqrt{\Delta}}{2a}\\\\ x=\dfrac{-1\pm \sqrt{25}}{2\cdot 1}\\\\ x=\dfrac{-1\pm 5}{2}\\\\ \begin{array}{rcl} x=\dfrac{-1-5}{2}&~\text{ ou }~&x=\dfrac{-1+5}{2}\\\\ x=\dfrac{-6}{2}&~\text{ ou }~&x=\dfrac{4}{2}\end{array}\\\\ \quad~~\boxed{\begin{array}{rcl} x=-3&~\text{ ou }~&x=2 \end{array}} \end{array}$


$\large\begin{array}{l} \text{Conjunto solu\c{c}\~ao: }S=\left\{-3,\,2 \right\}.\\\\\\ \text{D\'uvidas? Comente.}\\\\\\ \text{Bons estudos!} \end{array}$

Answer 2

Resposta:

(x+1). (x+1) = x=7

x² +x +1 = x +7

x² +2x +1 -x +7

x² +x -6 = 0 (simplificando)

Fórmula de báskara

A=1

B=1

C=-6

Calculando o Delta

Δ = b² -4.a.c -6

Δ = 1² -4.1 -6

Δ = 1 +24

Δ = 25 

B

-1 ≥  ∛25 ÷ 2

-1 ≥ 5÷2

x = 1 +5÷2 =2

x = -1 -5÷2 = -3