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

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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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 Selina Solution for Concise Mathematics for Class 10 ICSE (2020 (Latest))
Chapter 6: Solving (simple) Problems (Based on Quadratic Equations)
Exercise 6(A) | Q: 2 | Page no. 69
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The Sum of the Squares of Two Consecutive Natural Numbers is 41. Find the Numbers. Concept: Quadratic Equations.
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