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Question

If a+b+c=3 and a>0,b>0,c>0, then the greatest value of a2b3c2 is

A
3102477
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B
3102777
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C
372477
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D
372474
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Solution

The correct option is A 3102477
Taking A.M and G.M of 7 numbers a2,a2,b3,b3,b3,c2,c2, we get

2a2+3b3+2c27{(a2)2(b3)3(c2)2}17
37(a2b3c2(22)(33)(22))17
3777a2b3c2(22)(33)(22)
a2b3c23102477
Greatest value of a2b3c2=3102477

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