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.

Explanation

To prove that \( x, y, z \) are in Arithmetic Progression (A.P.) given that \( a, b, c \) are in Geometric Progression (G.P.) and \( a^{1/x} = b^{1/y} = c^{1/z} \), we can follow these steps:

### Step 1: Set up the equation
Let us denote the common value of \( a^{1/x} = b^{1/y} = c^{1/z} \) as \( k \). Therefore, we can write:
\[ a^{1/x} = k, \quad b^{1/y} = k, \quad c^{1/z} = k \]

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