Please help me prove that this equation has no solutions

Question

$\sqrt{x^2+1}+\sqrt{x-1}=-3$. Been stuck on it for a while, having figured out nothing. After i raise both sides to the second power, i get an equation with x in 4 different powers, which i have no way of solving. Please do help if you can.

Answer 1

The principle square root of any positive number is never negative, therefore the sum of two non-negative terms cannot be negative.

Answer 2

HINT

Square roots are never negative

Answer 3

Note: $\sqrt{x} \ge 0,$ $\forall x \in \mathbb{R^+}$

Adding two non-negative numbers cannot result in a negative value.