Hello,
If you're trying to prove that there is a unique solution, then your method is good. And it's easy to prove because
If you want to find a, then that's more complicated I guess can you first confirm what you are looking for ?
, a is a real number.
What I did:
Let 0, 1)\mapsto \mathbb{R}, f(x)=\frac{\sqrt{1+2x}+4\sqrt{1-x}}{\sqrt{(1+2x)(1-x)}}\Rightarrow \displaystyle f(1-a)=f(a)" alt="\displaystyle f0, 1)\mapsto \mathbb{R}, f(x)=\frac{\sqrt{1+2x}+4\sqrt{1-x}}{\sqrt{(1+2x)(1-x)}}\Rightarrow \displaystyle f(1-a)=f(a)" />. I want to prove that f is injective/ strictly monotone.
Well, that is my idea, but anything else would be okay. Thanks in advance.