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Home » The sequence is: 2, 6, 18, 54, 162. - Coaching Toolbox

The sequence is: 2, 6, 18, 54, 162. - Coaching Toolbox

📅 May 4, 2026 👤 scraface

May 04, 2026

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So, $ g(u) = u^2 + 1 $.
Now substitute $ u = x^2 - 2 $:
g(x^2 - 2) = (x^2 - 2)^2 + 1 = x^4 - 4x^2 + 4 + 1 = x^4 - 4x^2 + 5
\boxed{x^4 - 4x^2 + 5}
Question: Let $ x, y, z $ be positive real numbers such that $ x + y +...
\frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x}.
Solution: We are to minimize the expression
subject to $ x + y + z = 1 $, with $ x, y, z > 0 $.
Apply the **Cauchy-Schwarz Inequality** in the following form:
\left( \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x} \right)(y + z + x...

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