JEE Advance - Mathematics (2004 - No. 16)
If $$a,\,b,c$$ are positive real numbers. Then prove that
$$${\left( {a + 1} \right)^7}{\left( {b + 1} \right)^7}{\left( {c + 1} \right)^7} > {7^7}\,{a^4}{b^4}{c^4}$$$
The given inequality is incorrect.
Applying AM-GM inequality to a+1.
Applying AM-GM inequality to b+1.
Applying AM-GM inequality to c+1.
Multiplying the three inequalities to get the desired result.