If XY= 10 and XY2 + X2Y + X + Y= 99, then by rearranging the equations and substituting known values, it can be determined that X + Y = 9. Squaring both sides of this equation yields X2 + Y2 = 81, so X2 + Y2 = 61.

1. 2 2
If XY= 10 and XY + X Y + X +
2 2
Y= 99, then X + Y = ?
1.) First rearrange the equation to
the following:
XY(X +Y) + (X + Y) = 99

2. 2.) Then substitute 10 for XY
and simplify.
10 (X + Y) + (X + Y) = 99
10X + 10Y + X + Y = 99
11X + 11Y = 99
X+Y=9

3. 3.) Then square [X + Y = 9].
2 2 2
X + 2XY + Y = 9
2 2
X + 20 + Y = 81
2 2
X + Y = 61