Question

the square of two consecutive integers differ by 13,then the largest is

Answer 1

Let one number be x
The other number = x+1
Square of the numbers = x² and (x+1)²
According to the Q
⇒ (x+1)² - x² = 13
⇒ x² + 2x +1 -x² = 13
⇒ 2x +1 = 13
⇒ 2x = 13 - 1
⇒ 2x = 12 
⇒ x = 12/2
∴ x = 6
∴ The numbers are 
   x = 6
   x+1 = 6+1 = 7

Answer 2

Let the two consecutive numbers are a and (a+1)
then A/q,
(a+1)² - a² = 13
⇒a² +1 +2a - a² = 13
⇒2a =12
⇒a =6
so, (a+1) = 7
numbers are 6 and 7
greatest number is 7