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\bigstar CORRECT QUESTION :

\star \bold{a^x=b^y=c^z,b^2=ac} . Then SHOW that  \bf{\frac{1}{x}+\frac{1}{z}=\frac{2}{y}}

\bigstar Solution :

\star Let ,

\bf{Let,\;a^x=b^y=c^z=k}\\\\ \implies\bf{a=k^{1/x},b=k^{1/y},c=k^{1/z}}

\star Now SUB. these in b²=ac , we get ,

\implies \bf{(k^{1/y})^2=k^{1/x}.k^{1/z}}\\\\\implies \bf{k^{2/y}=k^{1/x + 1/y}}

\star BASES are equal.So exponents must be equal.

\implies\bf{\frac{2}{y}=\frac{1}{x}+\frac{1}{z}}

Hence Proved


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