The sum of two numbers is 1000 and the difference between their square

1.	The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.
Answer» Let the numbers be ‘a’ and ‘b’ Given, of two numbers is 1000 and the difference between their squares is 256000 ⇒ a + b = 1000 ---- (1) and ⇒ a²– b² = 25600 ⇒ (a + b)(a – b) = 25600 [From 1] ⇒ 1000(a - b) = 256000 ⇒ a – b = 256 ----- (2) Adding (1) and (2) ⇒ 2a = 1256 ⇒ a = 628 From (1) 628 + b = 1000 ⇒ b = 1000 - 628 = 372

The sum of two numbers is 1000 and the difference between their squares is 256000. Find the numbers.

Answer»

Let the numbers be ‘a’ and ‘b’

Given, of two numbers is 1000 and the difference between their squares is 256000

⇒ a + b = 1000 ---- (1)

and

⇒ a²– b² = 25600

⇒ (a + b)(a – b) = 25600

[From 1]

⇒ 1000(a - b) = 256000

⇒ a – b = 256 ----- (2)

Adding (1) and (2)

⇒ 2a = 1256

⇒ a = 628

From (1)

628 + b = 1000

⇒ b = 1000 - 628 = 372