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the sum of 3 numbers in AP is 12 and sum of their squares is 56.Find the number 2,4,6.
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AP series :- a,a+d,a+2d,.....
a+a+d+a+2d = 12
3a+3d=12
a+d=4
=>> 2nd term =4
a^2 + (a+d)^2 + (a+2d)^2 =56
a^2 + 4^2 + a^2 +2ad + 4d^2 =56
2a^2 + 16 + 2ad +4d^2 =56
2a^2 + 2ad +4d^2 = 40
a^2 + ad + 2d^2 = 20
a^2 -ad +2ad +2d^2 =20
a(a-d) +2d(a+d) = 20
a-d = 20 or ---(1)
a+2d =20 or
a+d = 20 -----(2)
From (1) and (2)
(1) + (2) = 2a =40
=>> a = 20
a+d = 4
=>> 20 + d = 4
=>> d= -16
Therefore AP series is 20,4,-12
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