InterviewSolution
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InterviewSolution
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If `a,bgt0` then the maximum value of `(a^(3)b)/((a+b)^(4)),` isA. `(81)/(512)`B. `(27)/(256)`C. `(27)/(512)`D. `(81)/(256)` |
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Answer» Correct Answer - B Using `AMgeGM` for a, a, a, 3b, we get `(a+a+a+3b)/(4)ge(axxaxxaxx3b)^(1//4)` `implies" "(3(a+b))/(4)ge(3a^(3)b)^(1//4)` `implies" "(3^(4))/(4^(4))(a+b)^(4)ge3a^(3)b` `implies" "(27)/(256)ge(a^(3)b)/((a+b)^(4))` `implies" "(a^(3)b)/((a+b)^(4))le(27)/(256)" for all "a,bgt0.` |
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