\boxed{x^4 - 4x^2 + 5}
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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
- 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}.
- Solution: We are to minimize the expression
