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Home » Now find \( g(h(2)) = g(3) \): - Dachbleche24

Now find \( g(h(2)) = g(3) \): - Dachbleche24

📅 March 9, 2026 👤 scraface

Mar 09, 2026

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📌 g(u) = x^4 + 4x^2 + 5 = (u^2 - 4u + 4) + 4(u - 2) + 5

📌 g(u) = u^2 - 4u + 4 + 4u - 8 + 5 = u^2 + 1

📌 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 + z = 1 $. Find the minimum value of

📌 \frac{x^2}{y} + \frac{y^2}{z} + \frac{z^2}{x}.

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