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If x,y in R satisfy the equation x^2 + y...

If `x,y in R` satisfy the equation `x^2 + y^2 - 4x-2y + 5 = 0,` then the value of the expression `[(sqrtx-sqrty)^2+4sqrt(xy)]/((x+sqrt(xy))` is

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Verified by Experts

The correct Answer is:
`(sqrt(2 + 1))/(sqrt(2))`
`f(x, y) = ( x - 2)^(2) + (y - 1)^(2) = 0`
`rArr x = 2 and y = 1`
`therefore ((sqrt(x) - sqrt(y))^(2) + 4 sqrt(xy))/(x + sqrt(xy))`
= ` (sqrt(2 -1)^(2) + 4sqrt(2)^(2))/(2 + sqrt(2)) =(sqrt(2) + 1)^(2)/(sqrt(2)(sqrt 2 + 1)) = (sqrt(2) + 1)/(sqrt(2))`
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