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Home » Set \( h(t) = 0 \): \( -5t^2 + 20t + 5 = 0 \). - 500apps

Set \( h(t) = 0 \): \( -5t^2 + 20t + 5 = 0 \). - 500apps

📅 March 14, 2026 👤 scraface

Mar 14, 2026

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📌 Now express each term:

📌 \( \frac{y}{x - y} = \frac{b + z}{a} \)

📌 \( \frac{z}{y - z} = \frac{z}{b} \)

📌 \( \frac{z}{x - z} = \frac{z}{a + b} \)

📌 S = 1 + 2\left( \frac{b + z}{a} + \frac{z}{b} - \frac{z}{a + b} \right)

📌 = 1 + 2z\left( \frac{1}{a} + \frac{1}{b} - \frac{1}{a + b} \right) + 2\frac{b}{a}

📌 This still depends on \( z \). But since the original expression is homogeneous (scaling \( x, y, z \) by a constant does not change the value), we can set \( z = 1 \) without loss of generality.

📌 Let \( z = 1 \), \( y = 1 + b \), \( x = 1 + b + a \), with \( a, b > 0 \). Then:

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