Question

Prove that x=2 in 3^x + 4^x = 5^x?

Answer 1

Just substitute

LS = 3^x + 4^x
= 3^2 + 4^2 = 25
RS = 5^x = 5^2 = 25

so LS = RS

You probably should have recognized the simplest
Pythagorean triangle relationship,
3^2 + 4^2 = 5^2, so you have the right-angled triangle with sides
3, 4, and 5