12 and 13
To find the consecutive numbers whose squares have a difference of 25 ,set up the following equations:
- Let the two consecutive numbers be represented by ( x ) and ( x + 1 )
- The square of the first number ( x )² and the square of the second number ( x + 1 )²
According to the given condition,the difference between the squares is 25
So ( x + 1 )² - ( x)² = 25
Expanding the terms : x² + 2x + 1 - x² = 25
Simplify the equation :
2x + 1 = 25
2x = 25 -1
2x =24
x =12
Therefore the two consecutive numbers are 12 and 13.
You can verify by finding the squares of 12 and 13 and finding the difference between them.
