Look at the first equation. LHS is never negative, so neither is RHS. Similarly, Q, R, S are >=0 too.
Say you can order the unknowns P<Q<R<S. Then substituting P for Q in first equation would make LHS<3P. But the modified LHS=3Q by the second equation giving 3Q<3P, an impossibility. By extension the same is true for the other unknowns. Therefore they are all equal and the only solutions are the ones Jer noted: P=0 and P=1/3.
Posted by xdog
on 2015-07-21 11:27:32