# Can we prove these inequalities involving $a, b, c$ and $d$? Add to your resource collection Remove from your resource collection Add notes to this resource View your notes for this resource
Prove that, if $a$, $b$ are real, $ab\le \left(\frac{a+b}{2}\right)^2,$ and deduce that, if $a$, $b$, $c$, $d$ are positive, $abcd\le \left(\frac{a+b+c+d}{4}\right)^4,$ with equality only when all numbers are equal.
By giving $d$ a suitable value in terms of $a$, $b$, $c$, or otherwise, prove that, if $a$, $b$, $c$ are positive, $abc\le \left(\frac{a+b+c}{3}\right)^3.$