Question

2 sen ^ 2 - sen x - 1 = 0

Answer 1

Resposta:

$S=\{x\in \mathbb{R}/x=\frac{\pi }{2}+2k\pi ~ou~x=\frac{7\pi }{6} +2k\pi ~ou~x=\frac{11\pi }{65}+2k\pi , k\inZ\}$

Explicação passo a passo:

2sen²x - senx - 1 = 0

Δ = b² - 4ac

Δ = (-1)² - 4.2.(-1)

Δ = 1 + 8

Δ = 9

$senx= \frac{-b\pm\sqrt{\Delta} }{2a} \\\\senx=\frac{-(-1)\pm\sqrt{9} }{2.2}\\\\senx=\frac{1\pm3}{4}\\\\senx=\frac{4}{4}=1\implies x=\frac{\pi }{2}+2k\pi , ~k\in Z\\ou\\senx=-\frac{2}{4}=-\frac{1}{2}\implies x=\frac{7\pi }{6}+2k\pi ,~k\in Z \\ou\\x=\frac{11\pi }{6}+2k\pi ,~k\in Z$