Question

the difference of the squares of two numbers is 45.the square of the small number is 4 times the large number. what are tge numbers?​

Answer 1

AnswEr:-

Given:-

• The difference of the squares of two numbers is 45.the square of the small number is 4 times the large number.

To find:-

• value of the numbers?.

Solution:-

Let the larger number be x.

Then,

Square of the smaller number = 4x

Square of the larger number = x²

Then,

⇒ x² - 4x = 45

⇒ x² - 4x - 45 = 0

⇒ x² - 9x + 5x - 45 = 0

⇒ x(x - 9) + 5(x - 9) = 0

⇒ (x - 9) (x + 5) = 0

⇒ x - 9 = 0 or x + 5 = 0

⇒ x = 9, - 5.

When x = 9,

Square of smaller number = 4x = 4 × 9 = 36

Smaller number = ± 6

Thus, the numbers are 9 and 6 or 9 and - 6.

When x = - 5

Square of smaller number = 4x = 4 × (- 5) = - 20

Hence, the numbers are 9 and 6 or 9 and - 6.

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