Putting a= b=c won't work

Algebra Level 4

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 \[ \sqrt{n}\]

Give your answer as m×n

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