Answer:
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 = <u>549 </u>
