Each of P, Q and R is a positive real number satisfying this system of equations:

P + Q = 13, and:
Q² + R² - Q*R = 25, and:
P² + R² + P*R = 144

Find R.

(In reply to Solution by Brian Smith)

Perhaps a simpliest way combining the equations 2 and 3:

P-Q+R=119/13
And as P+Q=13:

R=288/13-2P

Replacing R in equation 3

169P^2-3744P+19536=0

P=8,41 R=5,33 Q=4,59 (only two decimal aprox).
Edited on June 11, 2016, 5:48 pm

Posted by armando on 2016-06-11 17:46:55