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Home » You Wont Believe How Easy It Is to Spot Duplicates in Your Excel Files! - Sterling Industries

You Wont Believe How Easy It Is to Spot Duplicates in Your Excel Files! - Sterling Industries

📅 April 18, 2026 👤 scraface

Apr 18, 2026

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📌 Thus, the equation \( x^3 - 4x + 2 = 0 \) has three real solutions, expressible in trigonometric form or as approximations.

📌 But to give **exact real solutions**, we use:

📌 Let \( x = 2\cos\theta \). Then:

📌 Using identity: \( 4\cos^3\theta - 3\cos\theta = \cos 3\theta \), but our equation is \( x^3 - 4x + 2 = 0 \).

📌 Try substitution: \( x = 2y \):

📌 Let \( y = \cos\theta \), then:

📌 4\cos^3\theta - 4\cos\theta + 1 = 0 \implies \cos 3\theta = \frac{1}{4}

📌 Using identity: \( \cos 3\theta = \frac{1}{4} \implies 3\theta = \pm \arccos\left(\frac{1}{4}\right) + 2k\pi \)

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