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Question
The sum of the squares of two consecutive natural numbers is 41. Find the numbers.
Solution
Let the numbers be x and x + 1.
From the given information,
x2 + (x + 1)2 = 41
2x2 + 2x + 1 – 41 = 0
x2 + x – 20 = 0
(x + 5)(x – 4) = 0
x = –5, 4
But, –5 is not a natural number.
So, x = 4.
Thus, the numbers are 4 and 5.
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