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

**Solution:**

Let us find the 2 numbers whose sum is 27 and product is 182.

For this, let us consider one of the numbers to be x. Then the other number will be 27 - x.

The product of the two numbers is given as 182. This means in terms of x this can be expressed as, x(27 - x) = 182

This can be written in the form of the following quadratic equation:

x(27 - x) = 182

x(27 - x) = 182

27x - x^{2} = 182

27x - x^{2} - 182 = 0

x^{2} - 27 x + 182 = 0 [Rearranging the terms and multiplying both sides by negative sign]

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

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

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

x - 13 = 0 and x - 14 = 0

x = 13 and x = 14

Therefore, the required numbers are 13, 14. In other words, the two numbers whose sum is 27 and product is 182 are 13 and 14.

**☛ Check:** NCERT Solutions for Class 10 Maths Chapter 4

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**Video Solution:**

## Find two numbers whose sum is 27 and product is 182

Class 10 Maths NCERT Solutions Chapter 4 Exercise 4.2 Question 3

**Summary:**

The 2 numbers whose sum is 27 and product is 182 are 13 and 14.

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