Question

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find the number whose sum is 27 and product is 182

Answer 1

Given:- sum of number is 27 and product of numbers is 182.

To Find:- the numbers.

Solution :-

Let assume that the first number be x

and second number be (27 − x)

According to given condition, the product of two numbers is 182.

So,

☛ x × (27 − x) = 182

⇒27x - x² = 182

⇒x² - 27x + 182 = 0

⇒x² - 14x - 13x + 182 = 0

⇒x (x − 14) – 13 (x − 14) = 0

⇒(x − 14) (x − 13) = 0

⇒x = 14 and 13

Hence, the first number is 14 or 13.

Now we have to find the second number which is equal to (27 - x)

⇒ 27 - x = 27 - 14 = 13

⇒ 27 - x = 27 - 13 = 14

Hence, second numbers are 13 or 14.

Verification :

➸ Sum of numbers = 13 + 14 = 27

➸ Product of numbers = 13 × 14 = 182

Answer 2

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