AP/G.P

a,b,c,p are in G.P then a^x =b^y=c^z=p^Î¼ thren x,y,z,Î¼ are in
A.P
G.P
H.P
NONE

1 Answers

1357

Manish Shankar ·2008-12-29 00:46:09

a^x=b^y=c^z=p^Î¼=K

a=K^1/x, b=K^1/y, c=K^1/z, p=K^1/Î¼

b/a=c/b=p/c

K^1/y-1/x=K^1/z-1/y=K^1/1/Î¼-1/z

which gives
1/y-1/x=1/z-1/y=1/Î¼-1/z

so 1/x, 1/y, 1/z, 1/Î¼ are in AP

and x, y, z, Î¼ are in HP

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