A) H.P.
B) G.P.
C) A.P.
D) None of these
Correct Answer: A
Solution :
\[\log \,(x+z)+\log (x+z-2y)=2\log (x-z)\] \[\log (x+z)(x+z-2y)=\log {{(x-z)}^{2}}\] \[xz-xy-yz=-xz\]\[\Rightarrow 2xz=xy+yz\] Dividing by \[x\,y\,z,\] we get Þ \[\frac{2}{y}=\frac{1}{x}+\frac{1}{z}\] i.e., \[\frac{1}{x},\frac{1}{y},\frac{1}{z}\]are in A.P. Þ \[x,y,z\] are in H.P.
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