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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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