Question

If a^x = b^y = c^z and b^2 = ac, then prove
that 2/y=1/x+1/z
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Answer 1

ANSWER :

${a}^{x} = {b}^{y} = {c}^{z} \\ \\ \\ let \: \\ \\ \\ a = {k}^{ \frac{1}{x} } \\ \\ \\ b = {k}^{ \frac{1}{y} } \\ \\ \\ c = {k}^{ \frac{1}{z} } \\ \\ \\ {b}^{2} = ac \\ \\ \\ {( {k}^{ \frac{1}{y} }) }^{2} = {k}^{ \frac{1}{x} } \times {k}^{ \frac{1}{z} } \\ \\ \\ {k}^{ \frac{2}{y} } = {k}^{ \frac{1}{x} + \frac{1}{z} } \\ \\ \\ \frac{2}{y} = \frac{1}{x} + \frac{1}{z}$

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