document.write( "Question 122302: Find two positive real numbers that differ by 1 and have a product of 1. \n" ); document.write( "

Algebra.Com's Answer #89789 by Fombitz(32388) $\"\"$ $\"About$

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Let's call the first number A.
\n" ); document.write( "Let's call the second number B.
\n" ); document.write( "1. $\"B=A-1\"$ Differ by 1.
\n" ); document.write( "2. $\"AB=1\"$ Product equals 1.
\n" ); document.write( "Use B as a function of A of equation 1 in equation 2.
\n" ); document.write( " $\"AB=1\"$
\n" ); document.write( " $\"A%28A-1%29=1\"$
\n" ); document.write( " $\"A%5E2-A=1\"$
\n" ); document.write( " $\"A%5E2-A-1=0\"$
\n" ); document.write( "Using the quadratic formula,
\n" ); document.write( " $\"A+=+%28-%28-1%29+%2B-+sqrt%28+%28-1%29%5E2-4%2A%281%29%2A%28-1%29+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"A+=+%281+%2B-+sqrt%281%2B4+%29%29%2F%282%29+\"$
\n" ); document.write( " $\"A+=+%281+%2B-+sqrt%285%29%29%2F%282%29+\"$
\n" ); document.write( " $\"A%5B1%5D=+%281+%2B+sqrt%285%29%29%2F%282%29+\"$
\n" ); document.write( " $\"A%5B2%5D=+%281+-+sqrt%285%29%29%2F%282%29+\"$
\n" ); document.write( "Since $\"A%5B2%5D%3C0\"$ , we only have one solution.
\n" ); document.write( " $\"highlight%28A=+%281+%2B+sqrt%285%29%29%2F%282%29+%29\"$
\n" ); document.write( " $\"B=A-1\"$
\n" ); document.write( " $\"highlight%28B=%28sqrt%285%29%29%2F%282%29%29+\"$
\n" ); document.write( "Approximately,
\n" ); document.write( "A=1.618
\n" ); document.write( "B=0.618 \n" ); document.write( "

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