Question 17

If $$a$$, $$b$$, $$c$$ and $$d$$ are positive reals such that $$abcd=1$$, then the maximum value of $$a^2+b^2+c^2+d^2+ab+ac+ad+bc+bd+cd$$ is

Correct Answer: 0

Solution

Take $$a=b=t$$ and $$c=d=\frac{1}{t}$$, which keeps $$abcd=1$$. The expression then contains the term $$2t^2$$ and grows without bound as $$t$$ increases. Hence no finite maximum exists, so the source treats this as a bonus and $$0$$ is only a required placeholder.

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