If a,b,c,d are positive real numbers prove that bcd/a+ cda/b2 + dab/c2 + abc/d2 > a+b+c+d

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Please find below the solution to the asked query:

For positive numbers A.M.G.M.bcda2+cdab2+dabc23bcda2.cdab2.dabc23bcda2+cdab2+dabc23a2b2c2d3a2b2c23bcda2+cdab2+dabc23d33bcda2+cdab2+dabc23dbcda2+cdab2+dabc23d...iSimilarlycdab2+dabc2+abcd23a...iidabc2+abcd2+bcda23b...iiiabcd2+bcda2+cdab23c...ivAdd four equation3bcda2+cdab2+dabc2+abcd23a+b+c+dbcda2+cdab2+dabc2+abcd2a+b+c+d Proved

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