Question 130359
One number: x
The other number: y
The difference: x - y
They differ by 2:  x - y = 2
Their product is 20: x * y = 20


{{{x-y=2}}}, so:


{{{x=2+y}}}


{{{xy=20}}}


{{{(2+y)y=20}}}


{{{y^2+2y-20=0}}}


{{{y=(-2+-sqrt(4-(4)(1)(-20)))/2}}}


{{{y=(-2+-sqrt(84))/2}}}


{{{y=(-2+2*sqrt(21))/2}}} or {{{y=(-2-2*sqrt(21))/2}}}


{{{y=-1+sqrt(21)}}} or {{{y=-1-sqrt(21)}}}


But {{{y=-1-sqrt(21)<0}}}, and the problem asked for positive numbers so exclude this root.


{{{y=-1+sqrt(21)}}}


{{{x=2+y=2-1+sqrt(21)=1+sqrt(21)}}}


Check:


{{{1+sqrt(21)-(-1+sqrt(21))=2}}}


{{{(1+sqrt(21))(-1+sqrt(21))=-1+sqrt(21)-sqrt(21)+21=20}}} Answer checks.