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