The Difference Between the Squares of Two Consecutive Numbers is 31. Find the Numbers. - Mathematics

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Sum

The difference between the squares of two consecutive numbers is 31. Find the numbers.

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Solution

Let the numbers be x and x + 1 .
According to the question, 
\[(x + 1 )^2 - x^2 = 31\]
\[\text{ or }x^2 + 2x + 1 - x^2 = 31\]
\[\text{ or }2x = 31 - 1\]
\[\text{ or }x = \frac{30}{2}\]
or x = 15
Thus, the numbers are 15 and 16 .

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Chapter 9: Linear Equation in One Variable - Exercise 9.4 [Page 29]

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RD Sharma Class 8 Maths
Chapter 9 Linear Equation in One Variable
Exercise 9.4 | Q 2 | Page 29
Selina Concise Mathematics Class 8 ICSE
Chapter 14 Linear Equations in one Variable
Exercise 14 (C) | Q 8 | Page 170
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