x2 + y = 4
Square both sides of the equation.
(x2 + y)2 = 42
Expand the left side.
(x2 + y)(x2 + y) = 16
x4 + 2x2y + y2 = 16
Rearrange the terms on the left side.
2x2y + x4 + y2 = 16
Since x4 + y2 = 10 we can substitute 10 in for x4 + y2
2x2y + 10 = 16
Subtract 10 from both sides.
2x2y = 6
Divide both sides by 2
x2y = 3
x2 + y = 4
Square both sides of the equation.
(x2 + y)2 = 42
Expand the left side.
(x2 + y)(x2 + y) = 16
x4 + 2x2y + y2 = 16
Rearrange the terms on the left side.
2x2y + x4 + y2 = 16
Since x4 + y2 = 10 we can substitute 10 in for x4 + y2
2x2y + 10 = 16
Subtract 10 from both sides.
2x2y = 6
Divide both sides by 2
x2y = 3