Advanced MathMediumEvaluating a squared sum of fractional powers
Advanced Math practice question
For x > 0, the expression (x^(1/2) + x^(−1/2))² equals x + 2 + 1/x. What is the value of the expression when x = 4?
Answer: 25/4 or 6.25
At x = 4: 4 + 2 + 1/4 = 25/4 = 6.25. (Check: (2 + 1/2)² = (5/2)² = 25/4.)
Common wrong answers
- If you answered 4.25
- 4.25 is 4 + 1/4, forgetting the middle term 2.
- If you answered 8.5
- 8.5 doubles 4.25.
- If you answered 2.5
- 2.5 is x^(1/2) + x^(−1/2) before squaring.
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