若y+z-x/x+y-z=x+y-z/y+z-x=y+x-z/x-y+z=p,则p+p2+p3的值为/为分数线,p2为p的二次方,p3为p的三次方

Question

若y+z-x/x+y-z=x+y-z/y+z-x=y+x-z/x-y+z=p,则p+p2+p3的值为
/为分数线,p2为p的二次方,p3为p的三次方

Answer 1

p³=(z+x-y)/(y+z-x)*(x+y-z)/(z+x-y)*(y+z-x)/(x+y+z)= (x+y-z)/(x+y+z)
p²= (y+z-x)/(x+y+z) * (z+x-y)/(y+z-x)= (z+x-y)/(z+x+y)
p = (y+z-x)/(x+y+z)
p+p²+p³
=(y+z-x)/(x+y+z)+(z+x-y)/(z+x+y)+(x+y-z)/(x+y+z)
= (x+y-z+z+x-y+z-x+y)/(x+y+z)
=(x+y+z)/(x+y+z)
= 1