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

Solution: Let us say, first number be x and the second number is 27 – x. Therefore, the product of two numbers 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 Thus, either, x = -13 = 0 or x – 14 = 0 ⇒ x = 13 or x = 14 Therefore, if first number = 13, then second number = 27 – 13 = 14 And if first number = 14, then second number = 27 – 14 = 13 Hence, the numbers are 13 and 14.