document.write( "Question 394937: Inequalities ; If xy=25 find the least possible value for x+y, if both x and y are positive? \n" ); document.write( "

Algebra.Com's Answer #280286 by stanbon(75887) $\"\"$ $\"About$

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If xy=25 find the least possible value for x+y, if both x and y are positive?
\n" ); document.write( "---
\n" ); document.write( "x = 25/y
\n" ); document.write( "---
\n" ); document.write( "Substitute to get:
\n" ); document.write( "Sum = (25/y)+y
\n" ); document.write( "---
\n" ); document.write( "Sum = (25+y^2)/y
\n" ); document.write( "----
\n" ); document.write( "Find the derivative:
\n" ); document.write( "S' = [y(2y)-(25+y^2)]/y^2
\n" ); document.write( "--
\n" ); document.write( "S' =[y^2-25]/y^2
\n" ); document.write( "---
\n" ); document.write( "S' = 1-[(25)/y^2]
\n" ); document.write( "----
\n" ); document.write( "To find min/max solve S' = 0
\n" ); document.write( "1-[(25/y^2)] = 0
\n" ); document.write( "(25/y^2) = 1
\n" ); document.write( "y^2 = 25
\n" ); document.write( "y = 5
\n" ); document.write( "---
\n" ); document.write( "Substitute xy = 25
\n" ); document.write( "If y = 5, then x = 5
\n" ); document.write( "---
\n" ); document.write( "So, the minimum sum is 5+5 = 10
\n" ); document.write( "==================================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H. \n" ); document.write( "

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