Question

resolva (x+1)²=(x-1)²+x²-2.(x-1).x.cos 120°

Answer 1

$(x+1)^2=(x-1)^2+x^2-2\cdot (x-1)\cdot x\cdot \cos(120\º)$

$x^2+2x+1=x^2-2x+1+x^2-2\cdot (x-1)\cdot x\cdot (-\frac{1}{2})$

$x^2+2x+1=x^2-2x+1+x^2+(-2x+2)\cdot x\cdot (-\frac{1}{2})$

$x^2+2x+1=x^2-2x+1+x^2+(-2x^2+2x)\cdot (-\frac{1}{2})$

$x^2+2x+1=x^2-2x+1+x^2+\frac{2x^2-2x}{2}$

$x^2+2x+1=x^2-2x+1+x^2+x^2-x$

$x^2+2x+1=3x^2-3x+1$

$x^2+2x+1-3x^2+3x-1=0$

$-2x^2+5x=0$

$2x^2-5x=0$

$x(2x-5)=0$

$x_1=0$

$2x_2-5=0$

$2x_2=5$

$x_2=\frac{5}{2}$

Sendo assim a equação descrita assume o seguinte conjunto solução:

$S=\{0,\ \frac{5}{2}\}$