Question

当 X加Y等于-3 X的三次方加Y的三次方等于-18 X的七次方加Y的七次方等于?

Answer 1

x3+y3=(x+y)(x2-xy+y2)=-18

x2-xy+y2=6

(x+y)2-3xy=6

-3xy=6-9=-3

xy=1

x2+y2=6+xy=6+1=7

再平方

x4+2x2y2+y4=49

x4+y4=49-2=47

(x3+y3)(x4+y4)

x7+x3y4+x4y3+y7=-18*47=-846

x7+y7+x3y3(x+y)=-846

x7+y7+1*(-3)=-846

x7+y7=-843