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