Q:

Solving $ \sqrt{5x+1}+\sqrt{x-1}=2$

How to solve:
$$ \sqrt{5x+1}+\sqrt{x-1}=2$$
I can tell that 1 is a solution but I am not sure how to solve this algebraically, do i start by squaring both sides?

A:

Hint:
Since the expression involves $\sqrt{x-1}$, we must have $x \geq 1$. But in that case, $\sqrt{5x+1} \geq \sqrt6 > 2$. What does that imply?

