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Symmetric Polynomial Optimization with Constraint

2175ExpertAlgebraInequalities

HMIC 2024 · 2024

Suppose that $a, b, c$, and $d$ are real numbers such that $a+b+c+d=8$. Compute the minimum possible value of $$ 20\left(a^{2}+b^{2}+c^{2}+d^{2}\right)-\sum_{\text{sym}} a^{3} b, $$ where the sum is over all 12 symmetric terms.
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