Question

Utilizando as regras de produtos notáveis, descubra o valor de x na igualdade

( x + 1 )( x - 1 ) = ( 2x - 1 )2
_________ _________
2 8

Answer 1

$Pelo\;que\;deu\;pra\;entender:\\\frac{(x+1)(x-1)}{2}= \frac{(2x-1)*2}{8}\\ \\\frac{x^2-x+x-1}{2}= \frac{2x*2-1*2}{8}\\ \\8*(x^2-1)=(4x-2)*2\\\\8x^2-8=8x-4\\\\8x^2-8x-4=0\\Simplificando\;por\;8\\\\x^2-x-1/2=0\\\\Delta = (-1)^2-4*1*(-1/2)\\Delta = 3\\\\x=\frac{1 \pm \sqrt{3}} {2} \\\\x_1=\frac{1 + \sqrt{3}} {2}\\\\x_2=\frac{1 - \sqrt{3}} {2}$