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The sum of two numbers is 1
\n" ); document.write( "a + b = 1
\n" ); document.write( "a = (-b+1)
\n" ); document.write( " and the sum of their squares is 13.
\n" ); document.write( "a^2 + b^2 = 13
\n" ); document.write( "Replace a with (-b+1)
\n" ); document.write( "(-b+1)^2 + b^2 = 13
\n" ); document.write( "FOIL (-b+1)(-b+1)
\n" ); document.write( "b^2 - 2b + 1 + b^2 = 13
\n" ); document.write( "a quadratic equation
\n" ); document.write( "2b^2 - 2b - 12 = 0
\n" ); document.write( "simplify, divide by 2
\n" ); document.write( "b^2 - b - 6 = 0
\n" ); document.write( "Factors to
\n" ); document.write( "(b-3)(b+2) = 0
\n" ); document.write( "Two solution pairs, essentially the same
\n" ); document.write( "b = 3, then a = -2
\n" ); document.write( " and
\n" ); document.write( "b = -2, then a = 3
\n" ); document.write( ":
\n" ); document.write( "What is the sum of their cubes?
\n" ); document.write( " 3^3 + -2^3 = 27 - 8 = 19
\n" ); document.write( ":
\n" ); document.write( ":
\n" ); document.write( "Check in the 2nd equation
\n" ); document.write( "3^2 + -2^2 = 9 + 4 = 13\r
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