Question

Find two numbers whose sum is 27 and product is 182.

Answer 1

Here, sum of the numbers is 27.

             Let one of the numbers be x.

             ∴ Other number = 27 – x

             According to the condition,

             Product of the numbers = 182

             ⇒ x (27 – x) = 182

             ⇒ 27x – x² = 182

             ⇒ –x² + 27x – 182 = 0

             ⇒ x² – 27x + 182 = 0

             ⇒ x² – 13x – 14x + 182 = 0 –27 = (–13) + (– 14) and

             ⇒ x (x – 13) – 14 (x – 13) = 0 (– 13) × (– 14) = 182

             ⇒ (x – 13) (x – 14) = 0

             Either x – 13 = 0 ⇒ x = 13

             or x – 14 = 0 ⇒ x = 14

             Thus, the required numbers are 13 and 14.