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\[ \large \int_0^1 \dfrac{\arcsin \sqrt x}{x^2-x+1} \, dx \]

If the integral above is equal to \( \dfrac{\pi^2}{\sqrt n} \), find \(n\).

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Chinmay has had the idea of a function for some time, today we were able to get some stuff off of it.

we define (Chinmay's definition ...

\[\large 11z^{10} + 10iz^9 +10iz -11=0\]

Given that a complex number \(z\) satisfies the equation above, find \(|z|\).

Notations:

\[ \int \sqrt{\dfrac{1-\sqrt{x}}{1+\sqrt{x}}} \, dx = \ ? \]

How many positive integer solutions \((a, b)\) does the equation \[ a^2+b^2+(a+b)^2=b^3\] have, where \(0<b<2017?\)

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