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If a and b are positive numbers such tha...

If a and b are positive numbers such that `a^(2) + b^(2) = 4`, then find the maximum value of `a^(2) b`.

Text Solution

Verified by Experts

The correct Answer is:
`(16)/(3sqrt(3))`
Using `A.M ge G.M`., we get
`((a^2)/(2)+(a^3)/(2)+b^2)/(3g)ge((a^2)/(2)(a^2)/(2)b^2)^((1)/(3))`
`rArr (4)/(3) ge ((a^2b)^((2)/(3)))/(2^((2)/(3)))`
`rArr (a^2b) le ((4)/(3))^((3)/(2))xx 2=(16)/(3sqrt(3))`
Therefore , maximum value of `a^2b is (16)/(3sqrt(3))`.
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