Advanced MathVery hardSquared difference of fractional powers from a reciprocal sum
Advanced Math practice question
For x > 0, the expression (x^(1/2) − x^(−1/2))² equals x − 2 + 1/x. If x + 1/x = 7, what is the value of (x^(1/2) − x^(−1/2))²?
Answer: 5
x − 2 + 1/x = (x + 1/x) − 2 = 7 − 2 = 5.
Common wrong answers
- If you answered 7
- 7 forgets the −2.
- If you answered 9
- 9 adds 2 instead of subtracting.
- If you answered 49
- 49 squares 7, treating the expression as (x + 1/x)².
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