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Hanoi Open Mathematics Competition 2011 Junior Question 12

HOMC · Hanoi Open Mathematics Competition 2011 Junior

Question 12

Suppose \(a\gt 0,b\gt 0,a+b\le1\). Determine the minimum of \(M=\frac1{ab}+\frac1{a^2+ab}+\frac1{ab+b^2}+\frac1{a^2+b^2}\).