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If x^2+y x^2=4 then find the xamimum val...

If `x^2+y x^2=4` then find the xamimum value of `(x^3+y^3)/(x+y)`

Text Solution

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`x^(2)+y^(2)=4`
Let `x=2cos theta`,
`y=2 sin theta`
Now, `(x^(3)+y^(3))/(x+y)=x^(2)+y^(2)-xy`
`=4cos^(2)theta+sin^(2)theta-(2sin theta)(2cos theta)`
`=4-2sin 2 theta`
`rArr ((x^(3)+y^(3))/(x+y))_("max")=4-1(-1)=6`
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