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Find the minimum value of (x⁴ + 8)/x² for real x (x not equal to 0).

1. 4*sqrt(2)
2. 8
3. 2*sqrt(2)
4. 8*sqrt(2)

Correct answer: 4*sqrt(2)

Solution

Writing the expression as x² + 8/x², both terms are positive (using x²), so AM-GM gives a lower bound that is attained when the two terms are equal.

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