Question

The sum of two numbers is 1000 and the difference between their squares is 25600 then find the numbers

Answer 1

there is a mistake in the question and that mistake is 25600 not correct but 256000 is correct

sum of two numbers is 1000

let first number be x and second number be y

x+y = 1000
x = 1000-y...........(a)

take squares on both sides

x² = (1000 - y)²
x² = 1000000 + y² - 2000y.......(1)

difference between their squares is 256000

so, x²-y² = 256000
x² = y² + 256000..........(2)

equate (1) = (2)
y² + 1000000 - 2000y = y² + 256000
1000000 - 256000 = y² - y² + 2000y
744000 = 2000y
y = 744000/2000
y = 372 substitute in (a)
x = 1000 - 372
x = 628

first number is x = 628
second number is y = 372

Answer 2

Answer:

numbers are:

x = 512.8

y = 487.2

Step-by-step explanation:

sum of two numbers is 1000

let first number be x and second number be y

=>x+y = 1000

=>x = 1000-y...........(a)

take squares on both sides

=>x² = (1000 - y)²

=>x² = 1000000 + y² - 2000y

=>x²-y²= 1000000-2000y.......(1)

difference between their squares is 25600

=>x²-y² = 256000..........(2)

equate (1) = (2)

1000000 - 2000y = 25600

1000000 - 25600 = 2000y

974400 = 2000y

y = 974400/2000

y = 487.2 substitute in (a)

x = 1000 - 487.2

x = 512.8