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If \(x + \dfrac 1x = \sqrt 3\) , find the value of \(x^{15} + \dfrac1{x^{15}} = \ ? \) .

Find \(f'(0) \) if \( \large f(x) = \frac {e^{\sin(x)}}{\sec^2 (x)} \).

Find the smallest prime number \( n \), such that for all prime numbers \( p \geq n \), \( p^2 + 2 \) is always composite.

\[\large i{ z }^{ 3 }+z^{ 2 }-z+i=0\]

For \(i = \sqrt{-1}\), \(z\) is a complex number that satisfies the equation above. What is the value of ...

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