The sum of two numbers is 1000
Asked by admin @ in Math viewed by 318 People
The sum of two numbers is 1000 and the difference between their squares is 25600 then find the numbers
Answered by admin @
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
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