If a , b & 3 c are in arithmetic progression and a , b & 4 c are in geometric progression, then the possible values of a b are

Question

If a , b & 3 c are in arithmetic progression and a , b & 4 c are in geometric progression, then the possible values of a b are, 2 3 , 2, 3 2 , 1 2, 2 3 , 3 2, 1 2 , 2

MARKS App · Accepted Answer

a + 3 c = 2 b and b 2 = 4 a c ⇒ c = 2 b - a 3 = b 2 4 a ∴ 8 a b – 4 a 2 = 3 b 2 ⇒ 4 a 2 – 8 a b + 3 b 2 = 0 4 a 2 b 2 – 8 a b + 3= 0 ⇒ a b = 8 ± 64 - 4 × 4 × 3 2 × 4 a b = 2 ± 4 - 3 2 = 2 ± 1 2 = 3 2 , 1 2 .

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