Question 21269
LET THE NUMBER = X
ONE LESS THAN THE NUMBER =X-1
RECIPROCAL =1/X
SO X-1=1/X..MULTIPLYING BY X 
X(X-1)=1
X^2-X-1=0
USING THE QUADRATIC FORMULA
{{{x = (-b +- sqrt( b^2-4*a*c ))/(2*a) }}} ,WE HAVE A=1,B= -1,C= -1...SO
{{{x = (1 +- sqrt( 1+4 ))/(2) }}} 
HENCE THE NUMBERS ARE ..NOTE THAT THERE ARE 2 ANSWERS 
{{{x = (1 +- sqrt(5))/(2) }}}