X^4+y^4=53 and 2x^3y+3x^2y^2+2xy^3=14 find x+y

choices A)2 B)3 C)4 D)5 E)6

Wow! That's pretty crazy-looking, isn't it?

OK, here's the trick. It's recalling that
(x + y)^4 = x^4 + 4x^3 y + 6x^2 y^2 + 4xy^3 + y^4

and that that's just
(x^4 + y^4) + 2(2x^3 y + 3x^2 y^2 + 2xy^3)
= 53 + 2*14 = 81

so
(x + y)^4 = 81
x + y = 3, or -3, or 3i, or -3i

So the only choice that works is:
B) 3