Find the positive number which, when increased by 17, equals 60 times its reciprocal.

Problem restatementFind positive x such that x + 17 = 60 × (1/x).

Concept/ApproachForm a quadratic equation and solve using the discriminant.

Step-by-step calculation x + 17 = 60/x x² + 17x − 60 = 0 Discriminant D = 17² + 4×60 = 289 + 240 = 529 = 23² x = (−17 ± 23)/2 ⇒ x = 3 or x = −20 Positive solution ⇒ x = 3

Verification/Alternative3 + 17 = 20 and 60 × (1/3) = 20; equality holds.

Final Answer3