A- b- c - R-0 are in H-P- Then b-a-b-a-b-c-b-c is equal toA- 1B- 2C- -2D- -1

The correct option is B 2 b=2ac/a+c⇒b/a=2c/a+c ⇒b+a/b a=3c+a/c a Similiarly b/c=2a/a+c⇒b+c/b c=3a+c/a c ∴b+a/b c+b+c/b c=3a+c (3c+a)/a c=2(a c)/a c=2 ...

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Byju's Answer

Standard XII

Mathematics

Derivative

a, b, c ∈ R-0...

Question

$a, b, c ϵ R$ -{0} are in H.P. Then $\frac{b + a}{b - a} + \frac{b + c}{b - c}$ is equal to

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Solution

The correct option is B
2

$b = \frac{2 a c}{a + c} \Rightarrow \frac{b}{a} = \frac{2 c}{a + c} \Rightarrow \frac{b + a}{b - a} = \frac{3 c + a}{c - a}$
Similiarly $\frac{b}{c} = \frac{2 a}{a + c} \Rightarrow \frac{b + c}{b - c} = \frac{3 a + c}{a - c}$
$∴ \frac{b + a}{b - c} + \frac{b + c}{b - c} = \frac{3 a + c - (3 c + a)}{a - c} = \frac{2 (a - c)}{a - c} = 2$

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a,b,cϵR -{0} are in H.P. Then b+ab−a+b+cb−c is equal to

The correct option is B 2 b=2aca+c⇒ba=2ca+c⇒b+ab−a=3c+ac−a Similiarly bc=2aa+c⇒b+cb−c=3a+ca−c ∴b+ab−c+b+cb−c=3a+c−(3c+a)a−c=2(a−c)a−c=2

$a, b, c ϵ R$ -{0} are in H.P. Then $\frac{b + a}{b - a} + \frac{b + c}{b - c}$ is equal to