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Suppose a, b, c are in a.P and a^(2), b^...

Suppose `a, b, c` are in a.P and `a^(2), b^(2), c^(2)` are in G.P. If `a lt b lt c` and `a + b + c = 3/2` then the value of `a` Is

A

`(1)/(2sqrt2)`

B

`(1)/(2sqrt3)`

C

`(1)/(2) - (1)/(sqrt3)`

D

`(1)/(2) - (1)/(sqrt2)`

Text Solution

Verified by Experts

The correct Answer is:
D
Since, a, b and c are in an AP
Let `a = A -D, b = A, c = A + D`
Given, `a + b + c = (3)/(2)`
`rArr (A -D) + A + (A +D) = (3)/(2)`
`rArr 3A = (3)/(2) rArr A = (1)/(2)`
`:.` The number are `(1)/(2) -D, (1)/(2), (1)/(2) + D`
Also, `((1)/(2) -D)^(2), (1)/(4), ((1)/(2) + D)^(2)` are in GP.
`:. ((1)/(4))^(2) = ((1)/(2) - D)^(2) ((1)/(2) + D)^(2) rArr (1)/(16) = ((1)/(4) - D^(2))^(2)`
`rArr (1)/(4) - D^(2) = +- (1)/(sqrt2)`
`:. a = (1)/(2) +- (1)/(sqrt2)`
so, out of the given values, `a = (1)/(2) - (1)/(sqrt2)` is the right choice
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