For positive real numbers \(a,b,c,d,e\) prove that \[(a^3-a+2)(b^3-b+2)(c^3-c+2)(d^3-d+2)(e^3-e+2) \geq \left( S_4- S_2 +1 \right)^2\]

where \(S_4 = abcd + abce + abde + acde + bcde \\ S_2 = ab+ac+ad+ae+bc+bd+be+cd+ce+de\).

This problem is a part of Tessellate S.T.E.M.S.

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TopNewestShow solution please

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i have written the solution.

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I can't understand how to do it

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just break the brackets by simple multiplying and then use AM>=GM and then it will be done.

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how i solve the problem

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Please show the solution.

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i have written the solution

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