Question

已知x不等于y，且x的三次方减x等于5，y的三次方减y等于5，求x的平方加xy加y的平方

Answer 1

x³-Y³=x-Y,
所以
（x²+xy+Y²）（x-y）=x-Y,
所以
x²+xy+Y²=1.

Answer 2

x^3-x=5 (1)
y^3-y=5 (2)
(1)-(2)
x^3-y^3 -(x-y) = 0
x^3-y^3 = x-y
/
x^2+xy+y^2
=(x^3-y^3)/(x-y)
=(x-y)/(x-y)
=1