Question

(x – 1)2 - (x – 1) . (x + 4) = (x – 1) . (x + 1)

Answer 1

Resposta:

$\left(x-1\right)\cdot \:2-\left(x-1\right)\left(x+4\right)=\left(x-1\right)\left(x+1\right)\\\\\left(x-1\right)\cdot \:2-\left(x-1\right)\left(x+4\right)\\\\2x-2-\left(x-1\right)\left(x+4\right)\\\\2x-2-x^2-3x+4\\\\-x^2-x+2\\\\-x^2-x+2=x^2-1\\\\\mathrm{Adicionar\:}1\mathrm{\:a\:ambos\:os\:lados}\\\\-x^2-x+2+1=x^2-1+1\\\\\mathrm{Simplificar}\\\\-x^2-x+3=x^2\\\\\mathrm{Subtrair\:}x^2\mathrm{\:de\:ambos\:os\:lados}\\\\-x^2-x+3-x^2=x^2-x^2\\\\\mathrm{Simplificar}\\\\-2x^2-x+3=0$

$\mathrm{Para\:}\quad a=-2,\:b=-1,\:c=3\\\\x_{1,\:2}=\frac{-\left(-1\right)\pm \sqrt{\left(-1\right)^2-4\left(-2\right)\cdot \:3}}{2\left(-2\right)}\\\\\sqrt{\left(-1\right)^2-4\left(-2\right)\cdot \:3}\\\\\sqrt{\left(-1\right)^2+4\cdot \:2\cdot \:3}\\\\x_{1,\:2}=\frac{-\left(-1\right)\pm \:5}{2\left(-2\right)}\\\\\mathrm{Separe\:as\:solucoes}\\\\x_1=\frac{-\left(-1\right)+5}{2\left(-2\right)}\\\\\:x_2=\frac{-\left(-1\right)-5}{2\left(-2\right)}$

$\mathrm{As\:solucoes\:para\:a\:equacao\:de\:segundo\:grau\:sao:\:}\\\\x=-\frac{3}{2}\\\\\:x=1$

Answer 2

Resposta:

Está aí a conta espero ter ajudado ❤❤