If x > 0, xy = 1, then minimum value of x + y is?
- -1
- 1
- 2
- None of these
Explanation
Given xy = 1 and x > 0:
y = 1/x
We want to minimize x + y = x + 1/x.
Let's find the minimum value:
Let f(x) = x + 1/x
f'(x) = 1 - 1/x² = 0 for minimum
x² = 1
x = 1 (since x > 0)
f(1) = 1 + 1/1 = 2
The minimum value of x + y is 2.
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