Question

以知X+Y=4,X*2+Y*2=10,求X*3+Y*3,X*4+Y*4的值

Answer 1

x+y=4,x^2+y^2=(x+y)^2-2xy=10

xy=3

x^3+y^3=(x+y)(x^2-xy+y^2)=4*(10-3)=28

x^4+y^4=(x^2+y^2)^2-2x^2*y^2=100-2*9=82