Question

the sum of two numbers is 1000, and th difference Between their squares is 25600, then the numbers are​

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..

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Answer 2

ANSWER:

• The numbers are 512.8 and 487.2.

GIVEN:

• The sum of two numbers is 1000

• The difference Between their squares is 25600.

TO FIND:

• The two numbers.

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

$\blue{\underline{\boxed{\large{\bold{ \red{(A - B)^2= (A^2 -2AB + B^2)}}}}}}$

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.