How to solve $x^2=x!$

Question

If $x^2=x!$ , what are the values of $x$? And this equation too, if $x!=120$, we know that here $x=5$ because $5!=5×4×3×2×1=120$. This seems something like back calculation. Is there any process to solve this type of equation normally?

Answer 1

$x! >x(x-1)(x-2) >x^{2}$ for $x \geq 4$ so you only have to check if the equation holds for $x=1,2,3$.