Use Power mean inequality

$c^2 = a^2 + b^2 => c^n = c^{n-2}a^2 + c^{n-2}b^2 > a^n + b^n$.

SAUDITYA wrote: $c^2 = a^2 + b^2 => c^n = c^{n-2}a^2 + c^{n-2}b^2 > a^n + b^n$. is the same as that meant by : tarzanjunior wrote: Use Power mean inequality

$c^2=a^2+b^2$ $c^n=c^{2}c^{n-2}=a^{2}c^{n-2}+b^{2}c^{n-2}$ $c>a,b \Rightarrow c^{n-2}>a^{n-2} \wedge c^{n-2}>b^{n-2}$ $c^n=a^{2}c^{n-2}+b^{2}c^{n-2}>a^{2}a^{n-2}+b^{2}b^{n-2}=a^n+b^n$ $\blacksquare$