Question

已知x+y=5,xy=2,求下列各式的值：(1)x2+y2 ；(2)(x－y)2.x8+y8的值是多少!

Answer 1

x^2+y^2=(x+y)^2-2xy=25-4=21

(x-y)^2=(x+y)^2-4xy=25-8=17

x^8+y^8=(x^4+y^4)^2-2x^4y^4=[(x^2+y^2)^2-2x^2y^2]^2-2(xy)^4

={[(x+y)^2-2xy]^2-2(xy)^2]^2-2(xy)^4

=(21^2-8)^2-2*16=187457