If x and Y belong to R +, 1 / x + 1 / y = 2, find the minimum value of X + 2Y

1/x+1/y=2
SO 2 (x + 2Y) = (1 / x + 1 / y) (x + 2Y)
=3+(2y/x+x/y)>=3+2√(2y/x*x/y)=3+2√2
So the minimum value of X + 2Y is (3 + 2 √ 2) / 2

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