the sum of two numbers is 1000, and th difference Between their squares is 25600, then the numbers are
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the sum of two numbers is 1000, and th difference Between their squares is 25600, then the numbers are
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ANSWER:
GIVEN:
TO FIND:
EXPLANATION:
Let the numbers be x and y.
x + y = 1000
x = 1000 - y
x² - y² = 25600
Substitute x = 1000 - y
(1000 - y)² - y² = 25600
1000000 - 2000y + y² - y² = 25600
1000000 - 2000y = 25600
Divide by 100 on both sides
10000 - 20y = 256
Divide by 2 on both sides
5000 - 10y = 128
Divide by 10 on both sides
500 - y = 12.8
y = 500 - 12.8
y = 487.2
Substitute y = 487.2 in x = 1000 - y
x = 1000 - 487.2
x = 512.8
HENCE THE NUMBERS ARE 512.8 AND 487.2.
VERIFICATION:
Substitute y = 487.2 and x = 512.8 in x² - y² = 25600
x² = (512.8)² = 262963.84
y² = (487.2)² = 237363.84
x² - y² = 262963.84 - 237363.84
x² - y² = 25600
HENCE VERIFIED.
Verified answer
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..