Review question

# 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

Ref: R7865

## Suggestion

By giving $d$ a suitable value in terms of $a$, $b$, $c$, or otherwise, prove that, if $a$, $b$, $c$ are positive, $abc\le \left(\frac{a+b+c}{3}\right)^3.$

The cube on the right hand side is surprising —surely we should still be left with a fourth power there after substituting in a value for $d$?

So this gives us a suggestion: perhaps if we can change the cube to a fourth power, we will have a better idea of what is going on?