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Home » You Won’t Believe How Richard Gere Transformed Hollywood With These Rare Movies! - Aurero

You Won’t Believe How Richard Gere Transformed Hollywood With These Rare Movies! - Aurero

📅 March 16, 2026 👤 scraface

Mar 16, 2026

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📌 \( N^2 + D^2 = x^6 - 6x^4 + 9x^2 + x^4 + 2x^2 + 1 = x^6 - 5x^4 + 11x^2 + 1 \)

📌 \( xD(N^2 + D^2) = x(x^2 + 1)(x^6 - 5x^4 + 11x^2 + 1) \)

📌 This leads to a high-degree polynomial equation. Instead, consider symmetry and degree.

📌 Note that \( f(x) \) is odd and rational of degree asymptotically 1 (since \( \deg N - \deg D = 3 - 2 = 1 \)), so \( f(f(x)) \) is a composition of rational functions of degrees 1 and 1, but numerator degree â 3 + 2 = 5? Actually, degree of numerator in \( f(f(x)) \) is \( \deg(N^3) = 9 \), and denominator degree \( D(N^2 + D^2) \) is degree \( 2(5) = 10 \)? Wait, more carefully:

📌 After clearing denominators, the equation \( f(f(x)) = x \) becomes a rational function equation, and the degree of the resulting polynomial can be estimated.

📌 Since \( f(x) \) is a rational function of degree \( \max(\deg ext{num}, \deg ext{den}) = 3 \), then \( f(f(x)) \) has degree at most \( 3 imes 3 = 9 \). So \( f(f(x)) - x = 0 \) is a rational equation whose numerator is a polynomial of degree at most 9.

📌 But since \( f(f(x)) \) is odd (as composition of odd functions), and \( x \) is odd, the equation \( f(f(x)) = x \) is equivalent to \( g(x) = 0 \) where \( g \) is a degree â¤ 9 polynomial, odd.

📌 Moreover, we know \( x = 0 \) is a solution.

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