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

The correct option is C H.P. nbsp;a,b,c are in H.P. ⇒1a,1b,1c are in A.P. ⇒a+b+ca,a+b+cb,a+b+cc are in A.P. ∵ Multiplying an A.P. with a constant (a+b+c), re ...

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Standard XII

Mathematics

Harmonic Mean

If a , b , c ...

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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G . P .

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H . P .

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None

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Solution

The correct option is C $H . P .$
$a, b, c$ are in H.P.
$\Rightarrow \frac{1}{a}, \frac{1}{b}, \frac{1}{c}$ are in A.P.
$\Rightarrow \frac{a + b + c}{a}, \frac{a + b + c}{b}, \frac{a + b + c}{c}$ are in A.P.
$∵$ Multiplying an A.P. with a constant $(a + b + c),$ resulting sequence will also be in A.P.
$\Rightarrow 1 + \frac{b + c}{a}, 1 + \frac{a + c}{b}, 1 + \frac{a + b}{c}$ are in A.P.
$\Rightarrow \frac{b + c}{a}, \frac{a + c}{b}, \frac{a + b}{c}$ are in A.P.
$\Rightarrow \frac{a}{b + c}, \frac{b}{a + c}, \frac{c}{a + b}$ are in H.P.

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If a,b,c are in H.P., then ab+c,bc+a,ca+b are in

The correct option is C H.P. a,b,c are in H.P. ⇒1a,1b,1c are in A.P. ⇒a+b+ca,a+b+cb,a+b+cc are in A.P. ∵ Multiplying an A.P. with a constant (a+b+c), resulting sequence will also be in A.P. ⇒1+b+ca,1+a+cb,1+a+bc are in A.P. ⇒b+ca,a+cb,a+bc are in A.P. ⇒ab+c,ba+c,ca+b are in H.P.

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