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

Sum

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

#### 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 .

Is there an error in this question or solution?

#### APPEARS IN

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