Question

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

Answer 1

Let first number = x
There second number = x+1
$\therefore$ According to the condition:
$(x+1{)}^2-(x{)}^2=31\Rightarrow x^2+2x+1-x^2=31\Rightarrow 2x=31-1=30$
$\Rightarrow x=\frac{30}{2}=15$
$\therefore$ First number = 15
and second number = 15+1=16
Hence numbers are 15,16
Check : $(16{)}^2-(15{)}^{2}256-225=31$
Which is given
$\therefore$ Our answer is correct.