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Question

The product of two consecutive natural numbers is 56. Find the numbers.

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Solution

Let the two consecutive natural numbers be x and (x+1).
From the given condition,
x(x+1)=56
x2+x=56
x2+x56=0
x2+8x7x56=0
x(x+8)7(x+8)=0
(x7)(x+8)=0
x7=0 or x+8=0
x=7 or x=8
8 is not a natural number.
So, x=7 and x+1=7+1=8.
Hence, the numbers are 7 and 8.

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