Question

Find two natural numbers such that difference of their square is 24

Answer 1

Answer:

(5,1) or (7,5)

Step-by-step explanation:

Let the two natural numbers be x and y

x² - y² = 24

(x+y)(x-y) = 24 ----(1)

24 can be written as:

24 = 6×4 = 8×3 = 12×2= 24×1

» (x+y)(x-y) = 6×4.

x+y = 6

x-y = 4

2x = 10

x = 5

y = 1

» (x+y)(x-y) = 8×3

x+y = 8

x-y = 3

2x = 11

x = 5/2. (not a natural number)

» (x+y)(x-y) = 12×2

x+y = 12

x-y = 2

2x = 14

x = 7

y = 5

» (x+y)(x-y) = 24×1

x+y = 24

x-y = 1

2x = 25

x = 25/2 (not a natural number)