Question

if a/ b=b/c then show that ,1/b=1/b-a +1/b-c​

Answer 1

Step-by-step explanation:

Given (a/b) = (b/c)

= > b^2 = ac -------- (1)

Therefore, a,b,c are in GP.

Now,

LHS = (1/b - c) + (1/b - a)

= (b - a) + (b - c)/(b - c)(b - a)

= b - a + b - c/(b^2 - ab - bc + ca)

= 2b - (a + c)/b^2 - b(a + c) + ca

= 2b - (a + c)/b^2 - b(a + c) + b^2 (from (1))

= 2b - (a + c)/2b^2 - b(a + c)

= 2b - (a + c)/ b(2b - (a + c)

= 1/b.

Hope this helps!