If x, y, z are in harmonic progression,then l | vedclass

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Question

(A) If $x, y, z$ are in harmonic progression,then $y = \frac{2xz}{x + z}$.Now,consider the expression $\log(x + z) + \log(x - 2y + z)$.$= \log[(x + z)

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$2 \log |x - z|$

Vedclass · Answer

(A) If $x, y, z$ are in harmonic progression,then $y = \frac{2xz}{x + z}$.Now,consider the expression $\log(x + z) + \log(x - 2y + z)$.$= \log[(x + z)(x - 2y + z)]$$= \log[(x + z)(x + z - 2(\frac{2xz}{x + z}))]$$= \log[(x + z)(x + z - \frac{4xz}{x + z})]$$= \log[(x + z)^2 - 4xz]$$= \log[x^2 + 2xz + z^2 - 4xz]$$= \log[x^2 - 2xz + z^2]$$= \log[(x - z)^2]$$= 2 \log |x - z|$

If $x, y, z$ are in harmonic progression,then $\log(x + z) + \log(x - 2y + z) = \dots$

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