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The Sum of the Squares of Two Consecutive Natural Numbers is 41. Find the Numbers. - Mathematics

Sum

The sum of the squares of two consecutive natural numbers is 41. Find the numbers.

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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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Selina Concise Maths Class 10 ICSE
Chapter 6 Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6 (A) | Q 2 | Page 69
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