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You can put this solution on YOUR website!
let x = one of the numbers and y = the other.
\n" ); document.write( "if x exceeds y by 5, then x = y + 5
\n" ); document.write( "the sum of their squares is 157.
\n" ); document.write( "this means x^2 + y^2 = 157
\n" ); document.write( "since x = y + 5, then replace x with y + 5 in that equation to get:
\n" ); document.write( "(y + 5)^2 + y^2 = 157
\n" ); document.write( "simplify to get:
\n" ); document.write( "y^2 + 10y + 25 + y^2 = 157
\n" ); document.write( "combine like terms to get:
\n" ); document.write( "2y^2 + 10y + 25 = 157
\n" ); document.write( "subtract 157 from both sides of the equation to get:
\n" ); document.write( "2y^2 + 10y - 132 = 0
\n" ); document.write( "divide both sides of this equation by 2 to get:
\n" ); document.write( "y^2 + 5y - 66 = 0
\n" ); document.write( "factor this quadratic equation to get:
\n" ); document.write( "(y + 11) * (y - 6) = 0
\n" ); document.write( "solve for y to get:
\n" ); document.write( "y = -11 or y = 6\r
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\n" ); document.write( "\n" ); document.write( "when y = 6, x = y + 5 = 11
\n" ); document.write( "when y = -11, x = y + 5 = -6\r
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\n" ); document.write( "\n" ); document.write( "when y = 6 and x = 11, then 6^2 + 11^2 = 36 + 121 = 157
\n" ); document.write( "when y = -11 and x = -6, then (-11)^2 + (-6)^2 = 121 + 36 = 157.\r
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\n" ); document.write( "\n" ); document.write( "your numbers can be:
\n" ); document.write( "(6 and 11) or (-11 and -6).\r
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