The difference of squares of two numbers is 45

Asked by admin @ 20/08/2021 in Math viewed by 321 People

The difference of the squares of two numbers is 45 the square of the smallest number is 4 times the larger number determine the numbers.

Answered by admin @ 20/08/2021

Answer:

Step-by-step explanation:

Solution :-

Let the larger number be x.

Then,

Square of the smaller number = 4x

Square of the larger number = x²

Difference of the squares of number = 45

According to the Question,

⇒ x² - 4x = 45

⇒ x² - 4x - 45 = 0

By using factorization method, we get

⇒ 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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