Question

If a,b,c are in hp then 1/(b-a)+1/(c-a) is

Answer 1

Question :-

If a,b,c are in AP then 1/(b-a)+1/(c-a) is ?

Solution:—

Given,

a , b , c are in AP .

$\bold{ \tt{So, \: \: b = \frac{a + c}{2} }}$

Now ,

$\large \color{blue} \bold{ \frac{1}{b - a} + \frac{1}{c - a} }$

$= \large\bold {\frac{1}{ \frac{a + c}{2} - a } + \frac{1}{c - a} }$

$= \large\bold { \frac{1}{ \frac{a + c - 2a}{2} } + \frac{1}{c - a} }$

$= \large\bold { \frac{1}{ \frac{c - a}{2} } + \frac{1}{c - a} }$

$= \large\bold { \frac{2}{ c - a } + \frac{1}{c - a} }$

$= \large\bold { \frac{2 + 1}{ c - a } }$

$= \large \boxed{\bold { \frac{3}{ c - a } }}$