For a >= b >= 1, show 3ab+4a^2+2ab^2+2a^2b^2+a^3b+a^3 >= 11a^2b+a+b

[Royal]

\(\displaystyle \mbox{Let }\, a,\, b\, \in\, \mathbb{R}^+\, \mbox{ such that }\, a\, \geq\, b\, \geq\, 1.\)

\(\displaystyle \mbox{Prove that }\, 3ab\, +\, 4a^2\, +\, 2ab^2\, +\, 2a^2b^2\, +\, a^3b\, +\, a^3\, \geq\, 11a^2b\, +\, a\, +\, b\)

 

[Deleted member 4993]

\(\displaystyle \mbox{Let }\, a,\, b\, \in\, \mathbb{R}^+\, \mbox{ such that }\, a\, \geq\, b\, \geq\, 1.\)

\(\displaystyle \mbox{Prove that }\, 3ab\, +\, 4a^2\, +\, 2ab^2\, +\, 2a^2b^2\, +\, a^3b\, +\, a^3\, \geq\, 11a^2b\, +\, a\, +\, b\)

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