document.write( "Question 131543: Find a number such that 1 less than the number divided by the reciprocal of the number is equal to 1. (Leave the answeres in exact form, that is with the square root.) \n" ); document.write( "

Algebra.Com's Answer #96120 by edjones(8007) $\"\"$ $\"About$

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let x be the number.
\n" ); document.write( "(x-1) / 1/x =1
\n" ); document.write( "(x-1) *x=1
\n" ); document.write( "x^2-x=1
\n" ); document.write( "x^2-x-1=0
\n" ); document.write( "x^2-x =1
\n" ); document.write( "x^2-x+ 1/4=1+ 1/4
\n" ); document.write( "(x- 1/2)^2=5/4
\n" ); document.write( "x- 1/2=+-sqrt(5/4)
\n" ); document.write( "x=1/2+-sqrt(5)/2
\n" ); document.write( "x=(1+sqrt(5))/2, x=(1-sqrt(5))/2
\n" ); document.write( ".
\n" ); document.write( "Ed \n" ); document.write( "

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