Two natural numbers differ by 3 and their product is 504. The numbers are [[1]] and [[2]].

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answer is 24, 21.

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Detailed Solution

Two natural numbers differ by 3 and their product is 504. The numbers are 21 and 24.
Given that difference between two natural numbers

= 3

and product of the natural numbers= 504.
Let’s assume that the two natural numbers are

m

and

m + 3

.
According to the given condition,

m (m + 3) = 504

⟹ m^{2} + 3 m = 504

⟹ m^{2} + 3 m - 504 = 0

⟹ m^{2} + 24 m - 21 m - 504 = 0

⟹ m (m + 24) - 21 (m + 24) = 0

⟹ (m - 21) (m + 24) = 0

⟹ m - 21 = 0 or m + 24 = 0

∴ m = 21 or m = - 24

Therefore,

m = 21

.
And

m + 3 = 21 + 3

\Rightarrow m + 3 = 24

Thus, the two natural numbers are 21 and 24.

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