Question 394937: Inequalities ; If xy=25 find the least possible value for x+y, if both x and y are positive?
Answer by stanbon(75887)   (Show Source):
You can put this solution on YOUR website! If xy=25 find the least possible value for x+y, if both x and y are positive?
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x = 25/y
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Substitute to get:
Sum = (25/y)+y
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Sum = (25+y^2)/y
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Find the derivative:
S' = [y(2y)-(25+y^2)]/y^2
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S' =[y^2-25]/y^2
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S' = 1-[(25)/y^2]
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To find min/max solve S' = 0
1-[(25/y^2)] = 0
(25/y^2) = 1
y^2 = 25
y = 5
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Substitute xy = 25
If y = 5, then x = 5
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So, the minimum sum is 5+5 = 10
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Cheers,
Stan H.
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