Question

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

Answer 1

The 2 numbers are 512.8 and 487.2.

Explanation:

Let the numbers be x and y, then:

x + y = 1000............(1)

x^2 - y^2 = 25600

(x + y)(x - y) = 25600

1000(x - y) = 25600

x - y = 25.6............(2)

Adding (1) + (2):

2x = 1025.6

x = 512.8

so y = 1000 - 512.8

y = 487.2.

Answer 2

512.8 + 487.2

Explanation:

Let the two numbers be x and y respectively. The sum of x and y is 1000:

`x+y=1000`

The difference between their squares is 25600:

`x^2-y^2=25600`

We two unknowns(x and y) and two equations and therefore we can solve for x or y:

Lets:

`x+y=1000`

and

`x^2-y^2=25600`

We can simplify the expression as:

`(x+y)\cdot{(x-y)}=25600`

We can substitute x+y=1000 into this expression:

`1000\cdot{(x-y)}=25600`

We can now write x in terms of y and vice verse, therefore:

`(x-y)=25600/1000=25.6`

`x=25.6+y`

We have simple expression and can substitute it into x+y=1000

`25.6+y+y=1000`

`y=974.4/2=487.2`

therefore x can be solved by using the value of y and substituting it into x+y=1000:

`x+487.2=1000`

`x=512.8`