Advanced MathVery hardA number and its reciprocal
Advanced Math practice question
The sum of a positive number and its reciprocal is 5/2. What is the larger of the two possible values of the number?
Answer: 2
x + 1/x = 5/2. Multiply by 2x: 2x² + 2 = 5x, so 2x² − 5x + 2 = (2x − 1)(x − 2) = 0. The values are 1/2 and 2; the larger is 2.
Common wrong answers
- If you answered 5
- 5 comes from x² = 5x with the constant dropped.
- If you answered 0.5
- 1/2 is the smaller of the two values.
- If you answered 2.5
- 2.5 is the given sum, not the number.
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