if $k - 1$ is the $G . M$ between $k - 2$ and $k + 1$ , then find the value of $k$

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Solution

G.M of $(k - 2) a n d (k + 1)$ is $(k - 1)$
${(k - 1)}^{2} = (k - 2) (k + 1) k^{2} - 2 k + 1 = k^{2} - k - 2 k = 3$

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