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$ab(a^2+b^2)=ab(9-2ab)=9ab-2(ab)^2$, let $ab=k$, maximum of $9k-2k^2$ is when $k=\frac{9}{4}$. Rest calculation is for you.
Di-hydric equation
Find the largest value that the expression can take $a^3b + b^3a$ where $a, b$ are non-negative real numbers, with $a + b = 3$
Equation
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