Final answer:
To demonstrate that x² - 8x + 20 is always positive, completing the square reveals that the expression simplifies to a square term plus a positive constant.
Explanation:
To show that the expression x² - 8x + 20 is always positive, we can complete the square. The given expression can be rewritten as (x - 4)² + 4. Since any square term is always non-negative, and adding a positive constant to it keeps it positive, we conclude that x² - 8x + 20 is always positive.
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