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A positive number is greater than its reciprocal by 15/4. What is the number?

Competition practiceAlgebra

A4
B1/4
C15/4
D5

Step-by-Step Solution

x - 1/ x = 15/4

⇒

4 x^{2} - 15 x - 4 = 0

⇒

(4 x + 1) (x - 4) = 0

. Since

x

is positive,

x = 4

(check: 4 − 1/4 = 15/4).

Answer: A) 4

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