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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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