Question

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

Answer 1

Answer:

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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