SOLUTION: Inequalities ; If xy=25 find the least possible value for x+y, if both x and y are positive?

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?
---
x = 25/y
---
Substitute to get:
Sum = (25/y)+y
---
Sum = (25+y^2)/y
----
Find the derivative:
S' = [y(2y)-(25+y^2)]/y^2
--
S' =[y^2-25]/y^2
---
S' = 1-[(25)/y^2]
----
To find min/max solve S' = 0
1-[(25/y^2)] = 0
(25/y^2) = 1
y^2 = 25
y = 5
---
Substitute xy = 25
If y = 5, then x = 5
---
So, the minimum sum is 5+5 = 10
==================================
Cheers,
Stan H.
RELATED QUESTIONS
If z and y are negative integers and x - y = 1, what is the least possible value for... (answered by TimothyLamb)

Given that x-y= 8•sqrt(2) and xy= 137, where x and y are both positive, find the value... (answered by ikleyn,greenestamps)

If 3x+y=90 and 10<=x<=25 what is the least possible value of y? And alss slove for d... (answered by Edwin McCravy)

For x and y positive integers, if xy > = 9, what is the smallest possible sum of x +... (answered by ikleyn)

If x and y are positive integers such that x=8, what is the maximum possible value of... (answered by Alan3354)

If x and y are positive integers, x + y < 15, and x > 5, what is the greatest possible... (answered by Edwin McCravy,JimboP1977)

If x and y are positive integers , x+y<15,and x>5, what is the greatest possible value (answered by Fombitz)

If x and y are positive integers , x+y<15, and x>5, what is the greatest possible... (answered by JBarnum)

if x = y^2 and y = x^2, what is the least possible real value of x^2 + x + 1, where x... (answered by richard1234)