Question

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

Answer 1

Let a number be x. 

Then the other number = 27 – x 

Product of the numbers = x(27 – x) = 27x – x² 

By problem 27x – x² = 182 

⇒ x² – 27x + 182 = 0 

⇒ x² – 14x – 13x + 182 = 0 

⇒ x(x- 14) – 13(x – 14) = 0

⇒ (x – 13) (x – 14) = 0 

⇒ x – 13 = 0 or x – 14 = 0 

⇒ x = 13 or 14. 

∴ The numbers are 13 or 14 ; 27 – 13 = 14 and 27 – 14 = 13.