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Home » \( \sqrt34 \approx 5.831 \), so \( x \approx -1 + 11.662 = 10.662 \) - Get link 4share

\( \sqrt34 \approx 5.831 \), so \( x \approx -1 + 11.662 = 10.662 \) - Get link 4share

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 x^2 - (a + b)x + ab = 0 \Rightarrow x^2 - 4x + 3 = 0

📌 Roots: \( x = rac{4 \pm \sqrt{16 - 12}}{2} = rac{4 \pm 2}{2} = 3, 1 \)

📌 So \( a, b = 1, 3 \) (up to order), both real.

📌 Then \( |a - b| = |1 - 3| = 2 \)

📌 Since the expression is symmetric and values real, and sum/square match, and discriminant non-negative, \( a, b \) are real.

📌 Define \( L(u) = u - rac{u^3}{3} \) for every real number \( u \). If \( n \) is a positive integer, define \( a_n \) by \( a_1 = rac{1}{2} \), \( a_{n+1} = L(a_n) \). Find \( \lim_{n o \infty} a_n \).

📌 We are given a recursive sequence:

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