Question 122302
Let's call the first number A.
Let's call the second number B. 
1.{{{B=A-1}}} Differ by 1.
2.{{{AB=1}}} Product equals 1.
Use B as a function of A of equation 1 in equation 2. 
{{{AB=1}}}
{{{A(A-1)=1}}}
{{{A^2-A=1}}}
{{{A^2-A-1=0}}}
Using the quadratic formula,
{{{A = (-(-1) +- sqrt( (-1)^2-4*(1)*(-1) ))/(2) }}} 
{{{A = (1 +- sqrt(1+4 ))/(2) }}} 
{{{A = (1 +- sqrt(5))/(2) }}} 
{{{A[1]= (1 + sqrt(5))/(2) }}} 
{{{A[2]= (1 - sqrt(5))/(2) }}}
Since {{{A[2]<0}}}, we only have one solution.
{{{highlight(A= (1 + sqrt(5))/(2) )}}} 
{{{B=A-1}}}
{{{highlight(B=(sqrt(5))/(2)) }}} 
Approximately,
A=1.618
B=0.618