Question 238452
{{{A-B=2}}}
{{{1/A+1/B=20/21}}}
From eq. 1
{{{A=B+2}}}
Substitute into eq. 2,
{{{1/(B+2)+1/B=20/21}}}
Multiply by {{{B(B+2)}}}
{{{B+(B+2)=(20/21)B(B+2)}}}
{{{2B+2=(20/21)B(B+2)}}}
Multiply by {{{21)}}}
{{{42B+42=20B(B+2)}}}
{{{42B+42=20B^2+40B)}}}
{{{20B^2-2B-42=0}}}
{{{10B^2-B-21=0}}}
{{{(5B+7)(2B-3)=0}}}
Two solutions:
{{{5B+7=0}}}
{{{B=-7/5}}}
.
.
{{{2B-3=0}}}
{{{B=3/2}}}
Since the solution only allows positive numbers, we'll only use B=3/2.
Now solve for A.
{{{A=B+2}}}
{{{A=3/2+4/2=7/2}}}
Check the solution.
{{{1/A+1/B=20/21}}}
{{{2/7+2/3=20/21}}}
{{{6/21+14/21=20/21}}}
{{{20/21=20/21}}}
The solution checks out.