document.write( "Question 102444: The sum of a number and its reciprocal is 5/2. What is the number and reciprocal? \n" ); document.write( "

Algebra.Com's Answer #74444 by Fombitz(32388) $\"\"$ $\"About$

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$\"X%2B1%2FX=5%2F2\"$
\n" ); document.write( " $\"X%5E2%2B1=%285%2F2%29%2AX\"$ Multiply both sides by X.
\n" ); document.write( " $\"X%5E2-%285%2F2%29%2AX%2B1=cross%28%285%2F2%29%2AX%29-cross%28%285%2F2%29%2AX%29\"$ Additive inverse of $\"%285%2F2%29%2AX\"$
\n" ); document.write( " $\"X%5E2-%285%2F2%29%2AX%2B1=0\"$ Quadratic equation.
\n" ); document.write( "We can solve this equation using the quadratic formula where the solution for \r
\n" ); document.write( "\n" ); document.write( " $\"aX%5E2%2Bb%2AX%2Bc=0\"$ is solved by\r
\n" ); document.write( "\n" ); document.write( " $\"x+=+%28-b+%2B-+sqrt%28+b%5E2-4%2Aa%2Ac+%29%29%2F%282%2Aa%29+\"$ \r
\n" ); document.write( "\n" ); document.write( "In this case $\"a=1\"$ , $\"b=-5%2F2\"$ , $\"c=1\"$
\n" ); document.write( " $\"x+=+%28-%28-5%2F2%29+%2B-+sqrt%28+%285%29%5E2%2F%282%29%5E2-4%2A1%2A1%29%29%2F%282%2A1%29+\"$ Substitute into the quadratic formula.
\n" ); document.write( " $\"2x+=+%285%2F2+%2B-+sqrt%28+25%2F4-4%29%29%29+\"$ Multiply both sides by 2, just for convenience.
\n" ); document.write( " $\"2x+=+%285%2F2+%2B-+sqrt%28+25%2F4-16%2F4%29%29%29+\"$ Subtract fractions in the square root, need same denominator.
\n" ); document.write( " $\"2x+=+%285%2F2+%2B-+sqrt%28+9%2F4%29%29%29+\"$ Simplify.
\n" ); document.write( " $\"2x+=+%285%2F2+%2B-++3%2F2%29+\"$
\n" ); document.write( "Two solutions are
\n" ); document.write( "1. $\"2x+=+%285%2F2+%2B++3%2F2%29+\"$
\n" ); document.write( "1. $\"2x=8%2F2\"$
\n" ); document.write( "1. $\"x=2\"$
\n" ); document.write( "and
\n" ); document.write( "2. $\"2x+=+%285%2F2+-+3%2F2%29+\"$
\n" ); document.write( "2. $\"2x+=+%282%2F2%29+\"$
\n" ); document.write( "2. $\"x+=+1%2F2%29+\"$
\n" ); document.write( "Check your answers
\n" ); document.write( " $\"X+%2B+1%2FX+=+5%2F2\"$
\n" ); document.write( " $\"2+%2B+1%2F2+=+5%2F2\"$
\n" ); document.write( " $\"5%2F2+=+5%2F2\"$
\n" ); document.write( "True, good answer.
\n" ); document.write( " $\"X+%2B+1%2FX+=+5%2F2\"$
\n" ); document.write( " $\"1%2F2+%2B+1%2F%281%2F2%29+=+5%2F2\"$
\n" ); document.write( " $\"1%2F2+%2B+2+=+5%2F2\"$
\n" ); document.write( " $\"5%2F2+=+5%2F2\"$
\n" ); document.write( "True, good answer. \n" ); document.write( "

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