Algebra

Question

0

11

1

+569

Let x and y be complex numbers. If x + y = 2 and xy = 7 - x^2 - y^2, then what is x^2 + y^2?

onyuIee Jan 7, 2025

+28

+1

Best AnswerWe can square both sides of the first given equation to get

$(x+y)^2=4$ . This can be simplified to

$x^2+y^2+2xy=4$ . Now, we can substitute xy into the equation and get

$x^2+y^2+14-2x^2-2y^2=4$ , which when simplified turns into

$x^2+y^2=10$ , so 10 Is the answer.

Owinner Jan 7, 2025

Owinner · Answer 1 · 2025-01-07T05:37:00

We can square both sides of the first given equation to get

$(x+y)^2=4$ . This can be simplified to

$x^2+y^2+2xy=4$ . Now, we can substitute xy into the equation and get

$x^2+y^2+14-2x^2-2y^2=4$ , which when simplified turns into

$x^2+y^2=10$ , so 10 Is the answer.