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Question

If a>0,b>0 and a+b=4, find the maximum value of ab.

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Solution

given a+b=4, a>0,b>0
We know that for a finite number of terms (real)
A.M G.M
Consider the terms to be a,b
A.M =a+b2,
G.M=ab
A.M G.M
a+b2ab
2ab
ab4
Maximum value of ab is 4

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