wise urchin
Find all triples of real numbers such that:
xy + yz + zx = 1
and
x^2y + z = y^2z + x = z^2x + y.
so I handled the first 2 cases that x=y=z and x=y≠z and it gives all solutions but there is a case that all 3 are different and if I solve this one the first 2 cases are pointless cuz the 3rd one solves it all
could somebody help me? my teacher said that there is no solutions in 3rd case but I don't know how to do it. please help
sinful sealBOT
hearty wyvern
Find all triples of real numbers such that:
xy + yz + zx = 1
and
x^2y + z = ...
If x,y,z are nonzero then you can write z=x(xy-1)/(y²-1), substitute it into the first equality, and factor out xy-1. Then you get x²+xy+y²=1 and analogously y²+yz+z²=1. Subtract these and get x+y+z=0, which is impossible, or x=z, which implies x=y=z.
hearty wyvern
Please don't post unchecked AI hallucinations like this one.
wise urchin
Please don't post unchecked AI hallucinations like this one.
wdym?