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If a, b and c are in H.P., then the valu...

If a, b and c are in H.P., then the value of `((ac+ab-bc)(ab+bc-ac))/(abc)^2` is

A

`((a+c)(3a -c))/(4a^2 c^2)`

B

`2/(bc)-1/b^2`

C

`2/(bc)-1/b^2`

D

`((a-c)(3a+c))/(4a^2c^2)`

Text Solution

Verified by Experts

The correct Answer is:
A, B
`(1/b+1/c-1/a)(1/c+1/a-1b)`
`=(1/b+1/c-2/b+1/c)(1/c+1/b-1/c)`
Also by eliminating b, we get the given expression
`((a+c)(3a-c))/(4a^(2)c^(2))`
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