document.write( "Question 811202: Find a quadratic equation whose roots differ by 1 and are reciprocals of each other. Find the roots of the equation. (Two answers.) \n" ); document.write( "
Algebra.Com's Answer #488709 by ankor@dixie-net.com(22740)\"\" \"About 
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ind a quadratic equation whose roots differ by 1
\n" ); document.write( "a, b
\n" ); document.write( "a = b + 1
\n" ); document.write( "and are reciprocals of each other.
\n" ); document.write( "a = \"1%2Fb\"
\n" ); document.write( "then
\n" ); document.write( "b + 1 = 1/b
\n" ); document.write( "mult by b
\n" ); document.write( "b^2 + b = 1
\n" ); document.write( "b^2 + b - 1 = 0
\n" ); document.write( "Using the quadratic formula:
\n" ); document.write( "b = -1.618
\n" ); document.write( "b = +.618
\n" ); document.write( "Using the positive solution: a = 1.618
\n" ); document.write( "FOIL
\n" ); document.write( "(x+.618)(x+1.618) = x^2 + 2.236x + 1
\n" ); document.write( "Two roots using the quadratic formula:
\n" ); document.write( "x = -1.618
\n" ); document.write( "x = -.618
\n" ); document.write( ":
\n" ); document.write( "Check on calc 1/1.618 = .618, and 1/.618 = 1.618\r
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