Question

if a,b,c $ϵ$ R,a,b,c $\ne$ 0, $\sum$ $a^2$ = $\sum$ab, then a,b,c are in

• A. A.P
• B. G.P
• C. H.P
• D. A.G.P

Answer 1

Answer: (A), (B), (C), (D)

The correct options are
A

A.P

B

G.P

C

H.P

D

A.G.P

$\sum$ $a^2$ = $\sum$ab

$\Rightarrow$ $a^2$ + $b^2$ + $c^2$ = ab + bc + ca

$\Rightarrow$ $a^2$ + $b^2$ + $c^2$ - ab - ac - bc = 0

$\Rightarrow$ $\frac{1}{2}\left[\right(a-b{)}^2+(b-c{)}^2+(c-a{)}^2]=0$

$\Rightarrow$ $(a-b{)}^2+(b-c{)}^2+(c-a{)}^2]=0$

$\Rightarrow$ a =b, b =c and c =a

Or a=b=c

$\Rightarrow$ Number are same

$\Rightarrow$ A.P,G.P,H.P and A.G.P