Answer:
2500
Step-by-step explanation:
Let the first square number be [tex]x^2[/tex] then the next square number is [tex](x+1)^2[/tex].
The difference between these two consecutive numbers is 99.
This implies that:
[tex](x+1)^2-x^2=99[/tex]
We expand to get:
[tex]x^2+2x+1-x^2=99[/tex]
Simplify:
[tex]2x=99-1[/tex]
[tex]2x=98[/tex]
Divide both sides by 2
[tex]x=49[/tex]
Therefore the value of the larger perfect number is
[tex](49+1)^2=50^2=2500[/tex].
