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Home » how to get the y-intercept - Coaching Toolbox

how to get the y-intercept - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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📌 |a - b|^2 = (a - b)(\overline{a} - \overline{b}) = |a|^2 + |b|^2 - a\overline{b} - \overline{a}b

📌 Not helpful unless complex conjugates known.

📌 Alternate: treat \( a \) and \( b \) as roots of quadratic:

📌 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.

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