# The difference of squares of two numbers is 180. The square of a smaller number is 8 times the larger number. Find the two numbers

**Solution:**

Let the larger number be x.

The square of the smaller number is 8 times the larger number = 8x.

The difference of squares of the two numbers is 180.

Square of larger number - Square of smaller number = 180

x^{2} - 8x - 180 = 0

x^{2} - 18x + 10x - 180 = 0

x(x -18) + 10(x - 18) = 0

(x -18)(x + 10) = 0

x - 18 = 0 and x + 10 = 0

x = 18 and x = - 10

If the larger number is 18, then square of smaller number = 8 × 18

Therefore, smaller number = ± √8 × 18

= ± √ (2 × 2 × 2 × 3 × 3 × 2)

= ± (2 × 2 × 3)

= ± 12

If larger number is - 10, then square of smaller number = 8 × (- 10) = - 80

The Square of any number cannot be negative.

Therefore, x = -10 is not applicable.

The numbers are 18, 12 (or) 18, - 12.

**Video Solution:**

## The difference of squares of two numbers is 180. The square of a smaller number is 8 times the larger number. Find the two numbers

### Class 10 Maths NCERT Solutions - Chapter 4 Exercise 4.3 Question 7:

The difference of squares of two numbers is 180. The square of a smaller number is 8 times the larger number. Find the two numbers

The difference of squares of the two numbers is 180. The square of a smaller number is 8 times the larger number than two numbers are 12, 18