Question

The Difference of two numbers is 8 and the difference of their squares is 208. Find

the numbers.​

Answer 1

Answer:-

Let the numbers be a and b.

Given:

Difference = 8

⟶ a - b = 8 -- equation (1)

Difference between their squares = 208

⟶ a² - b² = 208

• a² - b² = (a + b)(a - b)

⟶ (a - b)(a + b) = 208

Substitute the value of a - b from equation (1).

⟶ 8 * (a + b) = 208

⟶ a + b = 208/8

⟶ a + b = 26 -- equation (2).

Add equations (1) & (2).

⟶ a - b + a + b = 8 + 26

⟶ 2a = 34

⟶ a = 34/2

⟶ a = 17

Substitute the value of a in equation (1).

⟶ 17 - b = 8

⟶ 17 - 8 = b

⟶ 9 = b

∴ The required numbers are 17 & 9.

Answer 2

Answer:

let the two number be x , y

x - y = 8

x^2 - y^2 = 208

(x-y)(x+y) = 208

8(x+y) = 208

x + y = 26.

x = 26 - y

x = 8+y

Hence,

26 - y = 8 + y

2y = 18

y = 9.

x = 8 + y

x = 17.