Question

The difference of the squares of two positive numbers in 45 The square of the smaller number is four times the larger number. Find the numbers

1. 3 and 15
2. 9 and 5
3. 3 and 16
4. 9 and 6

Answer 1

Correct Answer - Option 4 : 9 and 6

Given:

Difference of the square of two positive numbers = 45

Square of smaller number = 4 × Larger number

Calculation:

Let the smaller positive number be x and the larger number be y

According to the question

x² = 4y      ----(1)

Also, y² - x² = 45

⇒ y² - 4y - 45 = 0

⇒ y² - 9y + 5y - 45 = 0

⇒ y(y - 9) + 5(y - 9) = 0

⇒ (y + 5)(y - 9) = 0

⇒ y = -5 is not possible because y is a positive number

⇒ y = 9

Substituting value of y in equation (1), we get

⇒ x2 = 4y = 4 × 9 = 36

⇒ x = 6

∴ The required two numbers are 9 and 6.