Question from chris, a student:

Find all real solutions (x,y,z,w) of the system of equations: 2y= x + x/17 2z= y + y/17 2w = z + z/17 2x= w + w/17

Chris,

2y = x + x/17 2y = 18/17 x

and thus

y = 18/34 x.

Likewise

z = 18/34 y w = 18/34 z x = 18/34 w.

Hence

x = 18/34 w x = 18/34(18/34 z) x = 18/34(18/34(18/34 y)) x = 18/34(18/34(18/34(18/34 x))).

Thus

x = (18^{4 }/ 34^{4}) x.

Solve for x.

Penny