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Which of the foliowing statement(s) is/a...

Which of the foliowing statement(s) is/are true? (A) If `a^x =b^y=c^z and a,b,c` are in GP, then x, y, z are in HP (B) If `a^(1/x)=b^(1/y)=c^(1/z)` and `a,b,c` are in GP, then `x,y,z` are in AP

Text Solution

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Let `a^(1//x)=b^(1//y)=c^(1//z)=m` Then,
`a=m^(x), b=m^(y)` and `c=m^(z)`.
Since a, b, c are in GP we have
`b^(2)=ac rArr (m^(y))^(2)=(m^(x)xxm^(z))`
`rArr m^(2y)=m^(x+z) rArr 2y=x+z`.
`:. x, y, x` are in AP.
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