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📅 May 17, 2026 👤 scraface

May 17, 2026

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📌 y = \frac{2x^2 - 3x + 1}{x^2 + 1}

📌 Multiply both sides by \(x^2 + 1\):

📌 y(x^2 + 1) = 2x^2 - 3x + 1

📌 yx^2 + y = 2x^2 - 3x + 1 \quad \Rightarrow \quad (y - 2)x^2 + 3x + (y - 1) = 0

📌 For \(x\) to be real, the discriminant of this quadratic must be non-negative:

📌 3^2 - 4(y - 2)(y - 1) \geq 0

📌 - 4(y^2 - 3y + 2) \geq 0

📌 - 4y^2 + 12y - 8 \geq 0

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