Question

If a,b,c are in Ap prove that (a-c)^2=4(a-b)(b-c)

Answer 1

hope this will help you ...

Answer 2

Thus $LHS=RHS$

Step-by-step explanation:

Given;

$a$,$b$,$c$ are in $AP$ then prove that $(a-c)^{2}=4(a-b)(b-c)$

Let,

$a=a_{1}$,$b=a_{1} +d$ and $c=a_{1} +2d$  where $d$ is common different

Now,

LHS:-

$(a-c)^{2}$

$=(a_{1} -a_{1}-2d)^{2}$

$=(-2d)^{2}$

$=4d^{2}$

RHS:-

$4(a-b)(b-c)$

$=4(a_{1}- a_{1}-d)(a_{1}+d-a_{1} -2d)$

$=4(-d)(-d)$

$=4d^{2}$

∴ $LHS=RHS$