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Solve for real x: x^(2/5) - 3*x^(1/5) + 2 = 0.

1. x = 1 or x = 32
2. x = 1 or x = 2
3. x = 32 or x = 243
4. x = 5 or x = 10

Correct answer: x = 1 or x = 32

Solution

Let t = x^(1/5). The equation becomes t² - 3t + 2 = 0, factoring as (t - 1)(t - 2) = 0, so t = 1 or t = 2. Then x = t⁵: t = 1 gives x = 1; t = 2 gives x = 2⁵ = 32.

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