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Home » You Won’t Believe How SquaredCircle Solved the Ultimate Math Mystery! - Coaching Toolbox

You Won’t Believe How SquaredCircle Solved the Ultimate Math Mystery! - Coaching Toolbox

📅 May 5, 2026 👤 scraface

May 05, 2026

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📌 Now substitute back \( N = x^3 - 3x \), \( D = x^2 + 1 \):

📌 \( N^2 = (x^3 - 3x)^2 = x^6 - 6x^4 + 9x^2 \)

📌 \( N^3 = (x^3 - 3x)^3 = x^9 - 9x^7 + 27x^5 - 27x^3 \)

📌 \( D^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1 \)

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

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

📌 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:

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