Question

the difference between the squares of the two consecutive numbers is 31. find the number

Answer 1

Let 1st consecutive number be x

Let 2nd consecutive number be x+1

So,

x+x+1=31

2x+1=31

2x=31-1

x=30/2

x=15

1st consecutive number=x=15

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

Numbers will be 15 and 16.

Answer 2

$\bf{\underline{\huge{ ANSWER}}}$

Let one number be x

Square = ( x )^2 = x^2

Next consecutive number = x + 1

Square = ( x + 1 )^2

{ Applying ( a + b )^2 = a^2 + b^2 + 2ab }

=> x^2 + 1 + 2x

Difference in their squares = 31

$\bf{\underline{\huge{ THE \: EQUATION \: FORMED}}}$

=> x^2 + 1 + 2x - x^2 = 31

=> 1 + 2x = 31

=> 2x = 31 - 1

=> 2x = 30

=> x = 30/2

=> x = 15

ANS

$\bf{\huge{ One \: number \: = \: 15}}$

$\bf{\huge{ Another \: number \: = \: 16}}$

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