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Class-9»Maths

If a^x=b^y=c^z & b² =ac

show that=y=2xz/(z+x)

$Let a^{x} = b^{y} = c^{z} = k \Rightarrow a = k^{\frac{1}{x}}, b = k^{\frac{1}{y}}, c = k^{\frac{1}{z}} Given b^{2} = a c \Rightarrow {(k^{\frac{1}{y}})}^{2} = k^{\frac{1}{x}} \times k^{\frac{1}{z}} \Rightarrow k^{\frac{2}{x}} = k^{\frac{1}{x}} \times k^{\frac{1}{z}} \Rightarrow k^{\frac{2}{y}} = k^{\frac{1}{x} + \frac{1}{z}} \Rightarrow \frac{2}{y} = \frac{1}{x} + \frac{1}{z} \Rightarrow \frac{2}{y} = \frac{x + z}{x z} \Rightarrow y = \frac{2 x z}{x + z}$

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