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Home » Thus, the ratio is $ oxed{\sqrt3} $. - Coaching Toolbox

Thus, the ratio is $ oxed{\sqrt3} $. - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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\( N^3 = (x^3 - 3x)^3 = x^9 - 9x^7 + 27x^5 - 27x^3 \)
\( D^2 = (x^2 + 1)^2 = x^4 + 2x^2 + 1 \)
\( N^2 + D^2 = x^6 - 6x^4 + 9x^2 + x^4 + 2x^2 + 1 = x^6 - 5x^4 + 11x^2...
\( xD(N^2 + D^2) = x(x^2 + 1)(x^6 - 5x^4 + 11x^2 + 1) \)
This leads to a high-degree polynomial equation. Instead, consider sym...
Note that \( f(x) \) is odd and rational of degree asymptotically 1 (s...
After clearing denominators, the equation \( f(f(x)) = x \) becomes a...
Since \( f(x) \) is a rational function of degree \( \max(\deg ext{nu...
But since \( f(f(x)) \) is odd (as composition of odd functions), and...
Moreover, we know \( x = 0 \) is a solution.

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