document.write( "Question 1059185: Assume x > 0 and y > 0. If the square root of xy = 5, what is the smallest positive sum of 4x + y? \n" ); document.write( "

Algebra.Com's Answer #674450 by Fombitz(32388) $\"\"$ $\"About$

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Define $\"Z=4x%2By\"$
\n" ); document.write( "You know that,
\n" ); document.write( " $\"sqrt%28xy%29=5\"$
\n" ); document.write( " $\"xy=25\"$
\n" ); document.write( " $\"x=25%2Fy\"$
\n" ); document.write( "Substituting,
\n" ); document.write( " $\"Z=4%2825%2Fy%29%2By\"$
\n" ); document.write( " $\"Z=100%2Fy%2By\"$
\n" ); document.write( "Now Z is a function of one variable.
\n" ); document.write( "Find the derivative and set it equal to zero to find the minimum.
\n" ); document.write( " $\"dZ%2Fdy=-100%2Fy%5E2%2B1=0\"$
\n" ); document.write( " $\"100%2Fy%5E2=1\"$
\n" ); document.write( " $\"y%5E2=100\"$
\n" ); document.write( " $\"y=10\"$
\n" ); document.write( "So then,
\n" ); document.write( " $\"x=25%2F10\"$
\n" ); document.write( " $\"x=5%2F2\"$
\n" ); document.write( "and
\n" ); document.write( " $\"Z=4%285%2F2%29%2B10\"$
\n" ); document.write( " $\"Z=10%2B10\"$
\n" ); document.write( " $\"Z=20\"$
\n" ); document.write( "You should technically calculate the second derivative and show that the extremum is a minimum. \n" ); document.write( "

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