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?