Question

If log2x²(1+x²) = 1, then find x.​

Answer 1

Explanation:

$log_{2}x^2(1+x^2)=1$

$x^2(1+x^2)=2^1=2$

$x^4 + x^2 -2 = 0$

$x^4 -x^2 +2x^2-2x=0$

$x^2(x^2 -1)+2x(x^2 -1)=0$

$(x^2+2x)(x^2-1)=0$

$x(x+1)(x-1)(x+2)=0$

In this case, however, only 1 and -1 are able to correctly substitute x.

Answer: x = 1 or x = -1