document.write( "Question 1019565: Among all pairs of numbers (x,y) such as 4x+y=17 find the pair of which the sum o squares x^2+y^2 is minimum. Write the answer as reduced fractions. \n" ); document.write( "
Algebra.Com's Answer #635567 by ankor@dixie-net.com(22740)\"\" \"About 
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Among all pairs of numbers (x,y) such as 4x+y=17 find the pair of which the sum o squares x^2+y^2 is minimum.
\n" ); document.write( " Write the answer as reduced fractions.
\n" ); document.write( ":
\n" ); document.write( "convert the equation to the slope intercept form
\n" ); document.write( "y = -4x + 17
\n" ); document.write( ":
\n" ); document.write( "x^2 + y^2
\n" ); document.write( "replace y with (-4x+17), put in the form of an equation
\n" ); document.write( "f(x) = x^2 + (-4x+17)^2
\n" ); document.write( ":
\n" ); document.write( "FOIL (-4x+17)(-4x+17)
\n" ); document.write( "f(x) = x^2 + 16x^2 - 68x - 68x + 289
\n" ); document.write( "Combine like terms
\n" ); document.write( "f(x) = 17x^2 - 136x + 289
\n" ); document.write( "The minimum occurs at the axis of symmetry; x = -b/(2a), where a=17, b=-136
\n" ); document.write( "x = \"-%28-136%29%2F%282%2A17%29\"
\n" ); document.write( "x = \"136%2F34\"
\n" ); document.write( "x = 4
\n" ); document.write( "Find y
\n" ); document.write( "y = -4(4) + 17
\n" ); document.write( "y = -16 + 17
\n" ); document.write( "y = 1
\n" ); document.write( ":
\n" ); document.write( "x^2 + y^2 minimum; x=4, y=1 or x=1, y=4
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