Question

a.p. and a2 , b2 , c2 are in g.p. if a < b < c and a + b + c = 3/4, then the value of a is

Answer 1

Answer:

value of a = 1/4 - 1/2√2

Step-by-step explanation:

Hi,

Given that a, b and c are in A.P.

Let the common difference of A.P be 'd', say (d > 0)

If second term is 'b',

then first term 'a' = b - d

third term 'c' = b + d

Given a + b + c = 3/4

⇒ b - d + b + b + d = 3/4

⇒ 3*b = 3/4

⇒ b = 1/4.

Given that a², b² and c² are in G.P,

⇒ b² = √a²c²

⇒ac = ± b²

⇒(1/4 - d)(1/4 + d) = ±1/16

⇒1/16 - d² = ±1/16

It cannot be 1/16, since d would become 0

Hence, 1/16 - d² = -1/16

⇒ d² = 1/8

⇒ d = 1/2√2

Hence, the value of a = 1/4 - 1/2√2.

Hope, it helps !