Question 944234
X=one positive number, Y is the other positive number
{{{X-Y=8}}};  {{{1/X + 1/Y =1/6}}}
X=Y+8 Add Y to each side of Equation 1 and substitute in Equation 2 
{{{1/(Y+8)+1/Y=1/6}}} Multiply each side by 6
{{{6/(Y+8)+6/Y=1}}} Subtract 6/Y from each side
{{{6/(Y+8)=1-6/Y}}}  convert right side to fraction
{{{6/(Y+8)=1(Y/Y)-6/Y}}}
{{{6/(Y+8)=Y/Y-6/Y}}}
{{{6/(Y+8)=(Y-6)/Y}}} Multiply each side by Y+8
{{{6=(Y-6)(Y+8)/Y}}} Multiply each side by Y
{{{6Y=(Y-6)(Y+8)}}} Multiply right side through
{{{6Y=Y^2+2Y-48}}} Subtract 6Y from each side
{{{0=y^2-4Y-48}}}*[invoke quadratic "Y", 1, -4, -48 ]
The positive answer is 9.2111 so ANSWER 1 Y=9.2111
X-Y=8
X-9.2111=8 Add 9.2111 to each side
X=17.2111 ANSWER 2 X=17.2111
FINAL ANSWER THE TWO POSITIVE NUMBERS ARE 17.2111 and 9.2111
CHECK 
1/X+1/Y=1/6
1/17.2111+1/9.2111=1/6
0.16667=1/6
0.16667=0.16667