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X and y be two real numbers such that x greater than zero and xy=1.The minimum value of x+y is

X and y be two real numbers such that x greater than zero and xy=1.The minimum value of x+y is

Grade:12th pass

1 Answers

Arun
25757 Points
4 years ago
x +y = x + 1/x
 
Now
 
(x² + 1)/x = f(x)
 
Now
 
Differentiation
 
2x² - x² -1 /x² = 0
 
x² -1 = 0
 
x = ±1
 
Now
Again differentiation
 
2/x³
 
It is positive at x = 1
 
Hence x+y will be minimum at x= 1
 
Now
 
x+y = 1 +1 = 2

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