If the harmonic mean between a and b is H,the | vedclass

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

Question

(C) Given that $H$ is the harmonic mean between $a$ and $b$,we have $H = \frac{2ab}{a + b}$.We need to evaluate the expression $\frac{1}{H - a} + \fra

Vedclass · Accepted Answer

$\frac{1}{a} + \frac{1}{b}$

Vedclass · Answer

(C) Given that $H$ is the harmonic mean between $a$ and $b$,we have $H = \frac{2ab}{a + b}$.We need to evaluate the expression $\frac{1}{H - a} + \frac{1}{H - b}$.Substituting the value of $H$:$\frac{1}{\frac{2ab}{a + b} - a} + \frac{1}{\frac{2ab}{a + b} - b} = \frac{1}{\frac{2ab - a(a + b)}{a + b}} + \frac{1}{\frac{2ab - b(a + b)}{a + b}}$$= \frac{a + b}{2ab - a^2 - ab} + \frac{a + b}{2ab - ab - b^2} = \frac{a + b}{ab - a^2} + \frac{a + b}{ab - b^2}$$= \frac{a + b}{-a(a - b)} + \frac{a + b}{b(a - b)} = \frac{a + b}{a - b} \left( \frac{1}{b} - \frac{1}{a} \right)$$= \frac{a + b}{a - b} \left( \frac{a - b}{ab} \right) = \frac{a + b}{ab} = \frac{a}{ab} + \frac{b}{ab} = \frac{1}{b} + \frac{1}{a}$.Thus,the value is $\frac{1}{a} + \frac{1}{b}$.

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

Similar Questions

If $a, b, c$ are three distinct positive real numbers which are in $H.P.$,then $\frac{3a + 2b}{2a - b} + \frac{3c + 2b}{2c - b}$ is

Write the seventh term of the following $GP$: $6, 12, 24, 48, \ldots$

If $n$ is odd or even,then the sum of $n$ terms of the series $1 - 2 + 3 - 4 + 5 - 6 + \dots$ will be

The sum of the series $\frac{3}{1! + 2! + 3!} + \frac{4}{2! + 3! + 4!} + \frac{5}{3! + 4! + 5!} + \dots + \frac{2008}{2006! + 2007! + 2008!}$ is equal to

Let $a_1, a_2, ..., a_{10}$ be a $G.P.$ If $\frac{a_3}{a_1} = 25$,then $\frac{a_9}{a_5}$ is equal to:

Vedclass Test Series

Exam Paper Generator

Online Exam Module