document.write( "Question 1136263: Among all pairs of numbers (x,y) such that 8x+2y=18, find the pair for which the sum of squares, x2+y2, is minimum. Write your answers as fractions reduced to lowest terms. \n" ); document.write( "
Algebra.Com's Answer #754041 by ankor@dixie-net.com(22740)\"\" \"About 
You can put this solution on YOUR website!
Among all pairs of numbers (x,y) such that 8x+2y=18, find the pair for which the sum of squares, x2+y2, is minimum.
\n" ); document.write( " Write your answers as fractions reduced to lowest terms.
\n" ); document.write( ":
\n" ); document.write( "8x + 2y = 18
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "4x + y = 9
\n" ); document.write( "y = -4x + 9
\n" ); document.write( ":
\n" ); document.write( "sum = x^2 + y^2
\n" ); document.write( "replace y with (-4x+9)
\n" ); document.write( "sum = x^2 + (-4x+9)^2
\n" ); document.write( "FOIL (-4x+9)(-4x+9)
\n" ); document.write( "sum = x^2 + 16x^2 - 36x - 36x + 81
\n" ); document.write( "sum = 17x^2 - 72x + 81
\n" ); document.write( "min occurs on the axis of symmetry; x = -b/(2a)
\n" ); document.write( "x = \"%28-%28-72%29%29%2F%282%2A17%29\"
\n" ); document.write( "x = \"72%2F34\"
\n" ); document.write( "x = \"36%2F17\"
\n" ); document.write( ":
\n" ); document.write( "find y
\n" ); document.write( "y = \"17%2836%2F17%29%5E2+-+72%7B%7B%7B36%2F17\" + 81
\n" ); document.write( "y = 17(\"1296%2F289%29+-+%7B%7B%7B2592%2F17\" + 81
\n" ); document.write( "y = \"1296%2F17\" - \"2592%2F17\" + \"1377%2F17\"
\n" ); document.write( "y = \"81%2F17\"
\n" ); document.write( ":
\n" ); document.write( "Minimum of x^2 + y^2: x = 36/17; y = 81/17\r
\n" ); document.write( "\n" ); document.write( "Looks pretty wild, I hope this is right, let me know. ankor@att.net
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