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If x,y,in R^(+) satisfying x+y=3, then t...

If `x,y,in R^(+)` satisfying `x+y=3`, then the maximum value of `x^2y` is _____________.

Text Solution

Verified by Experts

The correct Answer is:
4
We have `(2((x)/(y))+y)/(3)ge(((x)/(2))^2y)^(1//3)`
`rArr ((3)/(3))^3ge (x^2y)/(4)`
`x^(2) 4`
Therefore, maximum value of `x^2y` is 4.
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