Sometimes we use trigonometric identities to find the roots of an equation. For example, if \( \....

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Sometimes we use trigonometric identities to find the roots of an equation. For example, if \( \frac{3 x-x^{3}}{1-3 x^{2}}=1 \),
\( \mathrm{P} \)
then to find the value of \( x \), we put \( x=\tan \theta \) here and the equation will be \( \tan 3 \theta=\tan 45^{\circ} \). Now one possible value of \( \theta \) is \( 15^{\circ} \). Thus, the possible value of ' \( x \) ' is \( \tan 15^{\circ} \), which is \( (2-\sqrt{3}) \).
Based on this information, answer the following questions.
One root of the equation \( 4 x^{3}-3 x+\frac{1}{\sqrt{2}}=0 \) may be
(1) \( \frac{\sqrt{3}-1}{2 \sqrt{2}} \)
(2) \( \frac{\sqrt{3}+1}{2 \sqrt{2}} \)
(3) \( -\frac{1}{\sqrt{2}} \)
(4) \( \frac{\sqrt{5}-1}{4} \)


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