Find two numbers whose sum is 27 and product is 182.
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.
x(27 – x) = 182
- x2 + 27x - 182 = 0
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
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.