# Hey! What's that?

Calculus Level 5

Let $$f$$ be a double differentiable function and satisfy the condition $$f(0)=0, f(1)=0$$ and $\dfrac{d^2}{dx^2}\left (e^{-x}f(x)-x^2\right )>0\ \forall\ x\in (0,1)$

Then the sum of values of $$x\in (0,1)$$ such that $f(x)-3=(x^2-x)e^x$ is $$\phi$$

The number of ordered pair(s) $$(x,y)$$ of real numbers satisfying equation $1+x^4+2x^2\sin(\cos^{-1}y)=0$ is $$\zeta$$.

Calculate $$\zeta+\phi$$.

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