Q. 213.9( 7 Votes )

Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.

Answer :

Let the two natural numbers be x and y.

According to the question


x2 + y2 = 25(x + y) – – – – – (1)


x2 + y2 = 50(x – y) – – – – (2)


From (1) and (2) we get


25(x + y) = 50(x – y)


x + y = 2(x – y)


x + y = 2x – 2y


y + 2y = 2x – x


3y = x – – – – – (3)


From (2) and (3) we get


(3y)2 + y2 = 50(3y – y)


9y2 + y2 = 50(3y – y)


10 y2 = 100y


y = 10


From (3) we have,


x = 3y = 3.10 = 30


Hence the two natural numbers are 30 and 10.


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