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.), we need to show that \( 2y = x + z \).

### Step-by-Step Solution:

1. **Given Condition**: We start with the condition that \( a, b, c \) are in Geometric Progression (G.P.) and that \( a^{1/x} = b^{1/y} = c^{1/z} \). Let us denote this common value as \( k \). Therefore, we can write:
\[ a^{1/x} = k, \quad b^{1/y} = k, \quad c^{1/z} = k \]
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