Anyone know what is the next line of Magic Math Square????

Question

what is the next line ???? What is the Forumla for solve it?????????
3^2 + 4^2 = 5^2
10^2+11^2+12^2= 13^2+14^2
21^2+22^2+23^2+24^2=25^2+26 ^2+27^2

NOte: the next line, right side should be 5 number of square and left side is 4 number of square and both side result should equal...

Answer 1

(3)² + (4)² = (5)²

9 + 16 = 25

25 = 25

- - - - - - - -

(10)² + (11)² + (12)² = (13)² + (14)²

100 + 121 + 144 = 169 + 196

221 + 144 = 365

365 = 365

- - - - - - - - - -s-

Answer 2

n^2 + (n+1)^2 + (n+2)^2 + (n+3)^2 + (n+4)^2 =
(n+5)^2 + (n+6)^2 + (n+7)^2 + (n+8)^2

5n^2 + 20n + 30 = 4n^2 + 52n + 174

n^2 - 32n - 144 = 0

(n + 4)(n - 36) = 0

Thus, n = -4 or 36.

You only want the positive value, which is n = 36.

36^2 + 37^2 + 38^2 + 39^2 + 40^2 =
41^2 + 42^2 + 43^2 + 44^2

EDIT:

The formula for the first number
in each equation is: x(2x + 1) for x = 1,2,3, ...

x = 1 gives n = 3
x = 2 gives n = 10
x = 3 gives n = 21
x = 4 gives n = 36
x = 5 gives n = 55

So the next one would be:
55^2 + 56^2 + 57^2 + 58^2 + 59^2 + 60^2 =
61^2 + 62^2 + 63^2 + 64^2 + 65^2.

Answer 3

you would like to find an integer n such that
(n-4)^2+(n-3)^2+(n-2)^2+(n-1)^2+n^2 = (n+1)^2+(n+2)^2+(n+3)^2+(n+4)^2
so
(n+4)^2 - (n-4)^2 + (n+3)^2 - (n-3)^2 + (n+2)^2 - (n-2)^2 + (n+1)^2 - (n-1)^2 = n^2
so 16n+12n+8n +4n = n^2
so 40n = n^2
so n = 40

check
36^2+37^2+38^2+39^2+40^2 = 7230
41^2+42^2+43^2+44^2 = 7230