• 0
Guru

# The difference between the squares of two numbers is 45. The square of the smaller number is 4 times the larger number. Determine the numbers.

• 0

This question has been taken from Book:- ML aggarwal, Avichal publication, class10th, quadratic equation in one variable, chapter 5, exercise 5.5
This is an important ques and asked in

The difference between the squares of two numbers is 45.

The square of the smaller number is 4 times the larger number.

Determine the numbers.
Question no.6 , ML Aggarwal, chapter 5, exercise 5.5, quadratic equation in one variable, ICSE board,

Share

### 1 Answer

1. Let us consider the larger number be ‘x’

Smaller number be ‘y’

So according to the question,

x2 – y2 = 45 … (i)

y2 = 4x … (ii)

Now substitute the value of y in equation (i), we get

x2 – 4x = 45

x2 – 4x – 45 = 0

let us factorize,

x2 – 9x + 5x – 45 = 0

x(x – 9) + 5 (x – 9) = 0

(x – 9) (x + 5) = 0

So,

(x – 9) = 0 or (x + 5) = 0

x = 9 or x = -5

When x = 9, then

The larger number = x = 9

Smaller number = y => y2 = 4x

y = 4x = 4(9) = 36 = 6

When x = -5, then

The larger number = x = -5

Smaller number = y => y2 = 4x

y = 4x = 4(-5) = -20 (which is not possible)

∴ The value of x and y are 9, 6.

• 0