# Hello Algebra? It's Me Calculus!

Calculus Level 4

$\begin{cases}\displaystyle f(x) = x + \int_0^1 t (x+t) f(t) \, dt \\ g(x) = a \left( \dfrac{23}6 f(x) \right)^2 + b \left( \dfrac{23}6 f(x)\right) + c \end{cases}$

Let $$f$$ and $$g$$ be two functions as defined above, where $$a$$, $$b$$ and $$c$$ are non-zero constants and the coefficients of $$x^2$$, $$x$$ and $$1$$ in the function $$g(x)$$ are equal. Find $$\dfrac{b+c}a - 1$$.

×