Question

como se resuelve

(2x^{2} -1)^{2} = (1+2x) (1-2x) -1

Answer 1

Oi :)

$(2x^2-1)^2=(1+2x)(1-2x)-1 \\ \\ 4x^4-4x^2+1^2=1-2x+2x-4x^2-1 \\ \\ 4x^4-4x^2+4x^2+1=0 \\ \\ 4x^4+1=0 \\ \\ 4x^4=-1 \\ \\ x^4=- \frac{1}{4} \\ \\ x=_-^+ \sqrt[4]{ -\frac{1}{4} }$
$x= \frac{1}{2}+ \frac{i}{2} \ ou \\ \\ x= \frac{1}{2}- \frac{i}{2} \ ou \\ \\ x= -\frac{1}{2}+ \frac{i}{2} \ ou \\ \\ x= \frac{1}{2}- \frac{i}{2}$