If frac{a}{b}, frac{b}{c}, frac{c}{a} are in | vedclass

Name: Exam Paper Generator | JEE NEET Paper Generator | Vedclass
Brand: Vedclass
Rating: 5 (35 reviews)

Question

(A) Given that $\frac{a}{b}, \frac{b}{c}, \frac{c}{a}$ are in $H.P.$Therefore,their reciprocals $\frac{b}{a}, \frac{c}{b}, \frac{a}{c}$ are in $A.P.$T

Vedclass · Accepted Answer

$a^2b, c^2a, b^2c$ are in $A.P.$

Vedclass · Answer

(A) Given that $\frac{a}{b}, \frac{b}{c}, \frac{c}{a}$ are in $H.P.$Therefore,their reciprocals $\frac{b}{a}, \frac{c}{b}, \frac{a}{c}$ are in $A.P.$This implies $2 	imes (\frac{c}{b}) = \frac{b}{a} + \frac{a}{c}$.Multiplying both sides by $abc$,we get $2ac^2 = b^2c + a^2b$.This equation represents the condition for $a^2b, c^2a, b^2c$ to be in $A.P.$ because $2(c^2a) = a^2b + b^2c$ is equivalent to $2c^2a = a^2b + b^2c$.

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

Similar Questions

If $H$ is the harmonic mean between $p$ and $q$,then the value of $\frac{H}{p} + \frac{H}{q}$ is

If the harmonic mean between $a$ and $b$ is $H$,then the value of $\frac{1}{H - a} + \frac{1}{H - b}$ is

If $\cos \left(x-\frac{\pi}{3}\right), \cos x, \cos \left(x+\frac{\pi}{3}\right)$ are in a harmonic progression,then $\cos x=$

If $a, b, c$ are in harmonic progression,then $\frac{a-b}{b-c} = \dots$

If $\frac{1}{b + c}, \frac{1}{c + a}, \frac{1}{a + b}$ are in Arithmetic Progression $(AP)$,then $a^2, b^2, c^2$ are in which progression?

Vedclass Test Series

Exam Paper Generator

Online Exam Module