Question

the difference of squares of two consecutive numbers is 31 .the numbers are

Answer 1

Step-by-step explanation:

Let 1st con number x

Let 2nd con. number x+1

So,

x+x+1=31

2x+1=31

2x=31-1

x=30/2

x=15

1st con number=x=15

2nd con number=x+1=15+1=16

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Answer 2

Given:

Difference of squares of two consecutive numbers is 31

To find:

The numbers

Explanation:

Let the CONSECUTIVE NUMBERS be x and (x+1)

According to the information given,

$\longrightarrow \sf (x+1)^2-x^2=31$

$\boxed{\sf (a+b)^2=a^2+b^2+2ab}$

$\longrightarrow \sf x^2+1+2x-x^2=31$

$\longrightarrow \sf 2x=30$

$\longrightarrow\sf x=\dfrac{30}{2}$

$\boxed {\sf x=15}$

Therefore the two numbers are 15,16

Note:-

↔You can also assume the numbers as x and (x-1) as they are consecutive numbers

↔You will get the same answer