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Question

If a,b,c are positive numbers such that a+b+c=18, then the maximum value of a2b3c4 is 


A
21933
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B
22034
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C
21834
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D
21934 
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Solution

The correct option is D 21933
Given a+b+c=18 
(a2+a2)+(b3+b3+b3)+(c4+c4+c4+c4)=18 

Since A.M.G.M.
2(a2)+3(b3)+4(c4)9[(a2)2(b3)3(c4)4]1/9 
189[(a2)2(b3)3(c4)4]1/9 
29a2b3c4223344
a2b3c433219 

Mathematics

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