# Weird inequalities!

Algebra Level 5

$\large a^2 + b^3 + c^4$

It is given that $$a,b$$ and $$c$$ are positive real numbers such that $$a+b^2+c^3 = \dfrac{325}9$$.

If the minimum value of the expression above can be expressed as $$\dfrac PQ$$ for coprime positive integers $$P$$ and $$Q$$, find the value of $$P + Q$$.

×