X+Y=2,X平方+Y平方=6,求X六次方+Y六次方
问题描述：
X+Y=2,X平方+Y平方=6,求X六次方+Y六次方
答
(x+y)^2=4
x^2+2xy+y^2=4
xy=-1
x^6+y^6
=(x^2+y^2)(x^4-x^2y^2+y^4)
=(x^2+y^2)((x^2+y^2)^2-3x^2y^2)
=6*(36-3)
=6*33
=198