the three numbers whose sum is 18 are in ap if they are added by 6 9/2 3 respectively the sum of square of the numbers
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Let numbers are a-d, a ,a+d
A.T.Q. ,...
a - d + a + a + d = 18
3a = 18
a=6
again A.T.Q ,....
6 - d + 2, 6 + 4, 6 + d + 11 are in G.P.
so,..
8 - d, 10 and 17 + d are in G.P.
10/8 - d = 17 + d/10
(17 + d)(8 - d) = 100
136 + 8d - 17d - d^2 = 100
d^2 + 9d - 36 = 0
d^2 + 12d - 3d - 36 = 0
d(d + 12) - 3(d + 12) = 0
d = 3, -12
if d = 3
numbers are 6 - 3, 6, 6 + 3
if d = -12
numbers are 18, 6, -6
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