Question

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

Answer 1

Let first number = x

and The second number = x + 1

According to the condition,

$\therefore (x+1{)}^2-(x{)}^2=31\Rightarrow x^2+2x+1-x^2=31\Rightarrow 2x=31-1=30\Rightarrow x=\frac{30}{2}=15$

$\therefore$ First number = 15

and second number = 15 + 1 = 16

Hence, the numbers are 15, 16