Question

If log (x + z) + log(x – 2y + z) = 2 log(x – z), then x, y, z are in

• A. A.P
• B. G.P
• C. H.P
• D. A.GP

Answer 1

The correct option is C H.P

$log\left[\right(x+z)+log(x-2y+z\left)\right]=2log(x-z)=log(x–z{)}^2$ $\Rightarrow (x+z)(x-1y+z)=(x-z{)}^2\Rightarrow (x+z{)}^2-(x-z{)}^2=2y(x+z)$ $\Rightarrow 4xz=2y(x+z)\Rightarrow y=\frac{2xz}{x+z}$