# Putting a= b=c won't work

Algebra Level 5

Let a,b,c be positive real numbers so that $a^{4} + b^{4} +c^{4} =4$

Then let the maximum value of the expression $a^{2} b^{2} \sqrt{7} +c^{2} b^{2} 3$ be m and the maximum value of the expression $a \times c^{2} \times b$ be $\sqrt{n}$