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Let \(x_1,x_2,\) and \(x_3\) be roots of \(x^3-9x^2+11x-1=0.\) If \(y=\sqrt{x_1}+\sqrt{x_2}+\sqrt{x_3},\) find the value of \[\displaystyle |y^4-18y^2-8y|\]

Evaluate

\[ \int_{0}^{\infty} \frac{ \sin^4 x } { x^4 } \, \mathrm dx. \]

Details and assumptions

You may use the fact that ...

What value of \(N\) in the interval \( [0, 90] \) satisfies the following equation: ...

Given the following trigonometry equation:

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Solve equation below:

\[ \displaystyle a \sin |2z| + \log_5 (x \sqrt[8]{2 - 5x^8}) + a^2 = 0 \]

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