While walking by a classroom, Linda sees two perfect squares written on a blackboard. She notices that their difference is her favorite number, 99. She also notices that there are exactly two other perfect squares between them. What is the sum of the two perfect squares on the blackboard

549

Step-by-step explanation:

considering 'n²' to express first square on board.

Remember 'n' is an integer

Now expressing second square with (n+3) ² on the board.

(Therefore, The other two perfect squares in between are (n+1) ² and (n+2) ².

If asking for the difference that is 99:

(n+3) ² - n² = 99

Solving for n:

n² + 6n + 9 - n² = 99

6n + 9 = 99

6n = 90

n = 90/6

n = 15

So the perfect squares on the board are:

n² = > 15² = 225

(n+3) ²=> 18² = 324

The difference between the above is 99

and exactly two other perfect squares (16² = 256 and 17² = 289) are in between.

Thus, the sum of the two perfect squares on the blackboard is,

225 + 324 = 549

15^2

18^2