Advanced MathMediumA number plus its reciprocal
Advanced Math practice question
A number greater than 1 added to its reciprocal equals 5/2. What is the number?
Answer: 2
x + 1/x = 5/2 gives 2x² − 5x + 2 = 0, so (2x − 1)(x − 2) = 0 and x = 2 or 1/2. The number greater than 1 is 2.
Common wrong answers
- If you answered 5
- 5 uses 5 as the number and forgets the reciprocal.
- If you answered 1/2
- 1/2 is the other root, which is less than 1.
- If you answered 5/2
- 5/2 is the given sum.
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