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

Question

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

Accepted Answer

Let the two consecutive numbers be x and (x – 1)

So now,

x2 – (x-1)2 = 31

By using the formula (a-b)2 = a2 + b2 – 2ab

x2 – (x2 – 2x + 1) = 31

x2 – x2 + 2x – 1 = 31

2x – 1 = 31

2x = 31+1

2x = 32

x = 32/2

= 16

Two consecutive numbers are, x and (x-1) : 16 and (16-1) =15

∴ The two consecutive numbers are 16 and 15.

RD Sharma Solutions Class 8 Mathematics Solutions for Linear Equation in One Variable Exercise 9.4 in Chapter 9 - Linear Equation in One Variable