Such power? Much scare! Many wow!

Algebra Level 5

The roots of the cubic equation

x34x2+6x5=0x^3 - 4x^2 + 6x - 5 = 0

are p,q,rp,q,r. If

p3q4+r4+q3p4+r4+r3p4+q4=ab \large \frac {p^3}{q^4+r^4} + \frac {q^3}{p^4+r^4} + \frac {r^3}{p^4+q^4} = - \frac {a}{b}

for coprime positive integers a,ba,b. What is the value of a2ba-2b?

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