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Question

If a,b,c are non zero real numbers, then minimum value of the expression((a4+a2+1)(b4+7b2+1)(c4+11c2+1)(a2b2c2)) is

A
315
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B
351
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C
415
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D
451
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Solution

The correct option is B 351
((a4+a2+1)(b4+7b2+1)(c4+11c2+1)(a2b2c2))=(a2+1a2+1)+(b2+1b2+7)+(c2+1c2+11)
Using A.MG.M we know that x2+1x22
The minimum value of the expression will occur when all the terms are mininum,
=(2+1)(2+7)(2+11)=351

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