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
⇒ \(x^2 -27x +182 = 0\)
⇒ \(x^2 - 13x -14x +182 =0\)
⇒ \(x(x-13) -14 (x-13) =0\)
⇒ \((x-13)(x-14) = 0\)

x – 13 = 0 or x − 14 = 0
i.e., 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.