If a- b- c are in H-P- then a-b-c- b-c-a- c-a-b are inA- H-P-B- A-P-C- G-P-D- None of these

The correct option is A H.P.Given a,b,c ϵ H.P. So, 1/a,1/b,1/c ϵ A.P. a+b+c/a,b+c+a/b,c+a+b/c ϵ A.P. By using concept if a,b,c ϵ A.P. Then their reciprocals ar ...

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Byju's Answer

Standard XII

Mathematics

Inverse of a Function

If a, b, c ar...

Question

If a, b, c are in H.P., then $\frac{a}{b + c}, \frac{b}{c + a}, \frac{c}{a + b}$ are in

A.P.

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H.P.

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G.P.

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None of these

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Solution

The correct option is B H.P.
Given $a, b, c ϵ H . P .$
So, $\frac{1}{a}, \frac{1}{b}, \frac{1}{c} ϵ A . P .$
$\frac{a + b + c}{a}, \frac{b + c + a}{b}, \frac{c + a + b}{c} ϵ A . P .$
By using concept if $a, b, c ϵ A . P .$
Then their reciprocals are in H.P.

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Given $a, b, c ϵ H . P .$
So, $\frac{1}{a}, \frac{1}{b}, \frac{1}{c} ϵ A . P .$
$\frac{a + b + c}{a}, \frac{b + c + a}{b}, \frac{c + a + b}{c} ϵ A . P .$
By using concept if $a, b, c ϵ A . P .$
Then their reciprocals are in H.P.