# Find the maximum value

Let $$\displaystyle a, b, c$$ be positive real numbers such that $$\displaystyle a + b + c = 3$$. Determine, with certainty, the largest possible value of the expression:
$$\displaystyle \frac {a}{a^3+b^2+c}+\frac {b}{b^3+c^2+a}+\frac {c}{c^3+a^2+b}$$
well by symmetry of the expression you know that $a=b=c$ and since they sum to 3 you thus know that $a=b=c=1$