Listen NCERT Audio Books to boost your productivity and retention power by 2X.
Find two natural numbers, the sum of whose squares is 25 times their sum and also equal to 50 times their difference.
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.