Question

If a,b,c are be in H.P show that
a:a-b = a+c : a-c

Answer 1

@ikram002p

Answer 2

@ganeshie8

Answer 3

@iambatman

Answer 4

If a,b,c are in HP then....
\[\LARGE 2b = \frac{ac}{a+c}\]
is it so?

Answer 5

you wrote smt wrong

Answer 6

Yeah typo wait

Answer 7

a,b,c are in HP so
1/a,1/b,1/c are in AP
\[\LARGE \frac{2}{b}=\frac{1}{a}+\frac{1}{c}\]
\[\LARGE \frac{2}{b}= \frac{a+c}{ac}\]
\[\LARGE b= \frac{2ac}{a+c}\]

Answer 8

yes

Answer 9

To show:
\[\LARGE \frac{a}{a-b} = \frac{a+c}{ a-c }\]

Answer 10

\[\LARGE \frac{a}{a-\frac{2ac}{a+c}} = \frac{a+c}{ a-c }\]
Take LCM and simplify..
\[\LARGE \frac{a(a+c)}{a^2-{ac}} = \frac{a+c}{ a-c }\]
\[\LARGE \frac{\cancel{a}(a+c)}{\cancel{a}(a-{c})} = \frac{a+c}{ a-c }\]
hence proved

Answer 11

oh well, that didn't strike me

Answer 12

just keep following your previous steps