( √(2) -1)^(|x|)=\sin^2x+1

Question

`( √(2) -1)^(|x|)=\sin^2x+1`

Answer 1

`\sqrt2 -1\approx 0.4 \Rightarrow \sqrt2 -1 \in (0,1)`

`|x|` is always non-negative, so the range of
`(\sqrt2-1)^(|x|)` is
`(0,1]`
The range of
`\sin x` is
`[-1,1]` => the range of
`\sin^2x` is
`[0,1]` => the range of
`\sin^2x+1` is
`[1,2]`
The only common point of these two function is the one with y-coordinate = 1, so
`y=1`. Let's take one of these functions and find for which x, its value is equal to 1. I'll take the first one.

`(\sqrt2-1)^(|x|)=1\\ \Downarrow\\ |x|=0\\ x=0`
So,
`x=0` :)