The sum of two numbers is 1000 and the difference between their square

1.	The sum of two numbers is 1000 and the difference between their square is 256000. Find the numbers.
Answer» Let’s assume the two numbers be x and y. And also assume that x is greater than or equal to y. So as per the question, we can write the sum of the two numbers as x + y = 1000 ……….. (i) Again it’s given that, the difference between the squares of the two numbers, thus writing it x² – y² = 256000 ⇒ (x + y) (x – y) = 256000 ⇒ 1000(x - y) = 256000 ⇒ x – y = 256000/1000 ⇒ x – y = 256 ………….. (ii) By solving (i) and (ii), we can find the two numbers On adding the equations (i) and (ii), we get; (x + y) + (x - y) = 1000 + 256 ⇒ x + y + x – y =1256 ⇒ 2x = 1256 ⇒ x = 1256/ 2 ⇒ x = 628 Now, putting the value of x in equation (i), we get 628 + y =1000 ⇒ y = 1000 – 628 ⇒ y = 372 Hence, the two required numbers are 628 and 372.

The sum of two numbers is 1000 and the difference between their square is 256000. Find the numbers.

Answer»

Let’s assume the two numbers be x and y. And also assume that x is greater than or equal to y.

So as per the question, we can write the sum of the two numbers as

x + y = 1000 ……….. (i)

Again it’s given that, the difference between the squares of the two numbers, thus writing it

x² – y² = 256000

⇒ (x + y) (x – y) = 256000

⇒ 1000(x - y) = 256000

⇒ x – y = 256000/1000

⇒ x – y = 256 ………….. (ii)

By solving (i) and (ii), we can find the two numbers

On adding the equations (i) and (ii), we get;

(x + y) + (x - y) = 1000 + 256

⇒ x + y + x – y =1256

⇒ 2x = 1256

⇒ x = 1256/ 2

⇒ x = 628

Now, putting the value of x in equation (i), we get

628 + y =1000

⇒ y = 1000 – 628

⇒ y = 372

Hence, the two required numbers are 628 and 372.