Question

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

Answer 1

Here, sum of the numbers is 27.

Let one of the numbers be x.

∴ Other number = 27 – x

According to the condition,

Product of the numbers = 182

⇒ x (27 – x) = 182

⇒ 27x – x2 = 182

⇒ –x2 + 27x – 182 = 0

⇒ x2 – 27x + 182 = 0

⇒ x2 – 13x – 14x + 182 = 0 –27 = (–13) + (– 14) and

⇒ x (x – 13) – 14 (x – 13) = 0 (– 13) × (– 14) = 182

⇒ (x – 13) (x – 14) = 0

Either x – 13 = 0 ⇒ x = 13

or x – 14 = 0 ⇒ x = 14

Thus, the required numbers are 13 and 14.

Answer 2

Answer:

Let the two numbers be x and 27-x

According to question

x(27-x) = 182

27x-x square = 182

x^2 -27x+182 = 0

x^2-13x-14x+182 = 0

x(x-13) -14(x-13) = 0

Thus x-13=0 and x-14=0

Therefore x=13 and x=14

Hence the two numbers are 13 and 14.

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