Question

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

Answer 1

Two consecutive no.s are x and x + 1
squares of both the no.s is x^2 and (x + 1)^2
their difference is 31
The equation forms like this :
x^2 - [(x + 1)^2] = 31
x^2 - [ x^2 + 1^2 + 2 * x * 1] = 31
x^2 - [ x^2 + 1 + 2x] = 31
x^2 - x^2 - 1 - 2x = 31
- 1 - 2x = 31
- 2x = 31 + 1
- 2x = 32
x = 32/-2
x = - 16
x + 1 = -16 + 1 
         = - 15
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Answer 2

We have to find two consecutive numbers so take the

first consecutive number as 'x'

and second consecutive number as 'x+1'

So,

According to the question,

$\implies x+x+1=31\\\\\implies2x+1=31\\\\\implies2x=31-1\\\\\implies2x=30\\\\\implies x=\dfrac{30}{2}\\\\\implies x=\underline{\boxed{\bold{15}}}$

Firstly we have to verify that our answer is right

To verify answer we have to put value '15' at the place of 'x'

Lets do it

$\implies x+x+1=31\\\\\implies15+15+1=31\\\\\implies31=31$

Here, LHS=RHS

Hence, it is verified.

So, First consecutive number = 15

Second consecutive number = x+1 = 15+1 = 16