document.write( "Question 587949: The difference between a number and twice its reciprocal is 1. Find the number. (Hint: form a quadratic equation and solve) \n" ); document.write( "

Algebra.Com's Answer #374325 by KMST(5328) $\"\"$ $\"About$

You can put this solution on YOUR website!
$\"x-2%281%2Fx%29=1\"$
\n" ); document.write( "Multiplying both sides by x, we get
\n" ); document.write( " $\"x%5E2-2=x\"$ --> $\"x%5E2-x-2=0\"$
\n" ); document.write( "We can solve by factoring
\n" ); document.write( " $\"x%5E2-x-2=0\"$ --> $\"%28x-2%29%28x%2B1%29=0\"$ --> $\"x=2\"$ or $\"x=-1\"$
\n" ); document.write( "VERIFICATION:
\n" ); document.write( " $\"2-2%281%2F2%29=2-1=1\"$
\n" ); document.write( " $\"%28-1%29-2%281%2F%28-1%29%29=-1-2%28-1%29=-1%2B2=1\"$ \n" ); document.write( "

\n" );