Let’s assume the two numbers be x and y. And also assume that x is greater than or equal to y.\xa0So as per the question, we can write the sum of the two numbers as\xa0x + y = 1000 ……….. (i)\xa0Again it’s given that, the difference between the squares of the two numbers, thus writing it\xa0x2\xa0– y2\xa0= 256000⇒ (x + y) (x – y) = 256000⇒ 1000(x – y) = 256000\xa0⇒ x – y = 256000/1000\xa0⇒ x – y = 256 ………….. (ii)\xa0By solving (i) and (ii), we can find the two numbers\xa0On adding the equations (i) and (ii), we get;\xa0(x + y) + (x – y) = 1000 + 256\xa0⇒ x + y + x – y =1256\xa0⇒ 2x = 1256\xa0⇒ x = 1256/ 2\xa0⇒ x = 628\xa0Now, putting the value of x in equation (i), we get\xa0628 + y =1000\xa0⇒ y = 1000 – 628\xa0⇒ y = 372\xa0Hence, the two required numbers are 628 and 372.
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