The sum of 2 numbers ia …
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Gaurav Seth 3 years, 9 months ago
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.
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