Question

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

Answer 1

Let the first number be x and the second number is 27 - x.

Therefore, their product = x (27 - x)

It is given that the product of these numbers is 182.

Therefore, x(27 - x) = 182

⇒ x² – 27x - 182 = 0

⇒ x² – 13x - 14x + 182 = 0

⇒ x(x - 13) -14(x - 13) = 0

⇒ (x - 13)(x -14) = 0

Either x = -13 = 0 or x - 14 = 0

⇒ x = 13 or x = 14

If first number = 13, then

Other number = 27 - 13 = 14

If first number = 14, then

Other number = 27 - 14 = 13

Therefore, the numbers are 13 and 14.