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If a,b,c are in G.P and a^((1)/(x))=b^((...

If a,b,c are in G.P and `a^((1)/(x))=b^((1)/(y))=c^((1)/(z))`, prove that x,y,z are in A.P.

Text Solution

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Let `a^((1)/(x))=b^((1)/(y))=c^((1)/(z))=k`
`thereforea=k^(x),b=k^(y),c=k^(z)`
Since a,b,c are in G.P., `b^(2)` =ac
`(k^(y))^(2)=k^(x).k^(z)rArrk^(2y)=k^(x+z)`
`therefore2y=x+zrArrx,y,z` are in A.P.
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