Square root equation problem $2\sqrt{2x}-\sqrt{x-1}-\sqrt{x+7}=0$

Question

I was solving some equations and got to this one:

$$2\sqrt{2x}-\sqrt{x-1}-\sqrt{x+7}=0$$

I tried square the equation, but it seems that it only complicates the process.

Answer 1

Hint: Writing your equation in the form

$$2\sqrt{2x}=\sqrt{x-1}+\sqrt{x+7}$$ and squaring gives

$$8x=x-1+x+7+2\sqrt{x-1}\sqrt{x+7}$$ Can you finish? Simplifying and squaring once more we get $$9(x-1)^2=(x-1)(x+7)$$