17. Determine all real values of p and r which satisfy the following system of equations:

Question

p+pr+pr^2=26 ,p^2r+p^2r^2+p^2r^3=156

Any tips help, but please show your work.

Answer 1

p+pr+pr^2=26
p(1+r+r^2) = 26
26 = 2*13
2(1+3+9) = 26
p=2, r=3
4*3(1+3+9) = 156
There is also the solution that
2*9(1 + 1/3 + 1/9) = 26
so p = 18 and q = 1/3