Question

Sum of two no.Is 1000 and the difference between their squares is 256000. Find the no.

Answer 1

Answer:

628, 372

Step-by-step explanation:

Let two numbers be (1000 - x) and x        [∵ Sum of x and 1000 - x is 1000]

According to question

x² - (1000 - x)² = 256000

Applying a² - b² = (a + b)(a - b) in LHS, where a = x and  b = (1000 - x)

[x + (1000 - x)][x - (1000 - x)] = 256000

(1000) ( 2x - 1000) = 256000

Dividing both sides by 1000

2x - 1000 = 256

2x = 1256

x = 628

∴ Numbers are x = 628 and (1000 - 628) = 372

Desired numbers are 628 and 372