document.write( "Question 309221: 2 positive numbers the sum of whose squares is 16 and whose product is as large as possible \n" ); document.write( "

Algebra.Com's Answer #221113 by stanbon(75887) $\"\"$ $\"About$

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2 positive numbers the sum of whose squares is 16 and whose product is as large as possible
\n" ); document.write( "---------------------
\n" ); document.write( "Equations:
\n" ); document.write( "x^2 + y^2 = 16
\n" ); document.write( "Product = xy
\n" ); document.write( "------------------------
\n" ); document.write( "y = sqrt(16-x^2)
\n" ); document.write( "--------
\n" ); document.write( "Product = x*sqrt(16-x^2)
\n" ); document.write( "----
\n" ); document.write( "Take the derivative
\n" ); document.write( "dP/dx = x[(1/2)(16-x^2)^(-1/2)(-2x)] + [sqrt(16-x^2)]
\n" ); document.write( "----
\n" ); document.write( "dP/dx = [-x/sqrt(16-x^2)] + [sqrt(16-x^2)]
\n" ); document.write( "----
\n" ); document.write( "dP/dx = [-x + 16-x^2]/sqrt(16-x^2)
\n" ); document.write( "------
\n" ); document.write( "Solve -x+16-x^2 = 0
\n" ); document.write( "x^2+x-16 = 0
\n" ); document.write( "x = [-1+-sqrt(1+4*16)]/2
\n" ); document.write( "---
\n" ); document.write( "x = [-1+-sqrt(65)]/2
\n" ); document.write( "---
\n" ); document.write( "Positive solution:
\n" ); document.write( "x = 3.53
\n" ); document.write( "-------------
\n" ); document.write( "Substitute into x^2 + y^2 = 16
\n" ); document.write( "y = sqrt(16-x^2)
\n" ); document.write( "y = sqrt(16-12.4689)
\n" ); document.write( "y = 1.8791
\n" ); document.write( "==============================
\n" ); document.write( "Cheers,
\n" ); document.write( "Stan H.
\n" ); document.write( " \n" ); document.write( "

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