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 $(b+c), (c+a), (a+b)$ are in $H.P.$,then $a^2, b^2, c^2$ are in.......

The fifth term of the $H.P.$,$2, 2\frac{1}{2}, 3\frac{1}{3}, \dots$ will be

If the $7^{th}$ term of a harmonic progression is $8$ and the $8^{th}$ term is $7$,then its $15^{th}$ term is

When $\frac{1}{a} + \frac{1}{c} + \frac{1}{a - b} + \frac{1}{c - b} = 0$ and $b \ne a \ne c$,then $a, b, c$ are

The terms $\log _3 2, \log _6 2, \log _{12} 2$ are in:

Vedclass Test Series

Exam Paper Generator

Online Exam Module