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Home » Stop Settling—You’re The Best at Achieving Unstoppable Success! - Sourci

Stop Settling—You’re The Best at Achieving Unstoppable Success! - Sourci

📅 May 2, 2026 👤 scraface

May 02, 2026

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📌 To rationalize the denominator, multiply the numerator and the denominator by the conjugate of the denominator:

📌 R = \frac{4}{\sqrt{x} + 2} \times \frac{\sqrt{x} - 2}{\sqrt{x} - 2}

📌 R = \frac{4(\sqrt{x} - 2)}{(\sqrt{x} + 2)(\sqrt{x} - 2)}

📌 The denominator simplifies using the difference of squares:

📌 R = \frac{4(\sqrt{x} - 2)}{x - 4}

📌 \boxed{\frac{4(\sqrt{x} - 2)}{x - 4}}

📌 Question:** A patent attorney is reviewing a patent that involves a formula where \( p+q=10 \) and \( p^2+q^2=58 \). Find \( p^3 + q^3 \).

📌 We know the identity:

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