Question

The sum of 2 numbers is 9. The difference of their squares is also 9. The two numbers are ______.

विकल्प

• 6, 3

• 7, 2

• 5, 4

• 8, 1

Answer 1

The sum of 2 numbers is 9. The difference of their squares is also 9. The two numbers are 5, 4.

Explanation:

Using the identity,

a² − b² = (a − b)(a + b)

Here,

a + b = 9

a² − b² = 9

So,

(a − b)(a + b) = 9

(a − b)(9) = 9

∴ a − b = 1

We now have:

a + b = 9     ...(1)

a − b = 1     ...(2)

Adding equations (1) and (2),

(a + b) + (a − b) = 9 + 1

2a = 10

a = `10/2`

∴ a = 5

Substitute a = 5 into equation (1):

5 + b = 9

b = 9 − 5

∴ b = 4

Hence, the numbers are 5 and 4.