Question

已知：点（x，y）在直线y=-x+1上，且x2+y2=2，求x7+y7的值．

x+y=1,为什么x2+y2也等于1喃

Answer 1

由y=-x+1可得y+x=1
x2+y2=2
x7+y7也只能等于7了

追问

额 似乎不对吧

追答

是x的平方+y的平方吧 ∵x2+y2=2⇒1=(x+y)2=x2+y2+2xy=2+2xy⇒xy=-12，∴x3+y3=(x+y)3-3xy(x+y)=1-3×(-1/2)=5/2x4+y4=(x2+y2)2-2x2y2=4-2(-1/2)2=7/2，∴x7+y7=(x3+y3)(x4+y4)-x3y3(x+y)=5/2×7/2-(-12)3×1=71/8

Answer 2

7