Question

if a, b, c are in HP then prove that a-b/b-c=a/c​

Answer 1

Answer:

Step-by-step explanation:

LHS =  a - b / b-c

Since it is in HP so  b =2ac / a+ c

so putting  and solving we get,

= a^2 +ac -2ac / 2ac- ac - c^2

= a^2 - ac / ac - c^2

= a ( a -c ) / c ( a -c )

= a /c = RHS      proved.

Answer 2

Answer:

Given a, b, c are in hp

=1/a ,1/b ,1/c are in ap

=1/b - 1/a =1/c - 1/b

=a-b/ab =b-c/bc

=(a-b) c=(b-c) a

=a-b/b-c =a/c

Hence prove