数学难题系列（6）若非零复数x,y满足x2+xy+y2=0,求[x/(x+y)]2007+[y/(x+y)]2007的值.要具体过程.wu

Question

数学难题系列（6）
若非零复数x,y满足x2+xy+y2=0,求[x/(x+y)]2007+[y/(x+y)]2007的值.要具体过程.
wu

Answer 1

x^2+xy+y^2=0 得x^3=y^3 得x^2007=y^2007
x^2+xy+y^2=0 得x^2=-y(x+y) 得x+y=-x^2/y 得(x+y)^2007=-x^5014/y^2007=-x^2007
原式=2*x^2007/(x+y)^2007=2*x^2007/(-x^2007)=-2