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If a^x=b^y=c^z\ a n d\ b^2=a c , prove t...

If `a^x=b^y=c^z\ a n d\ b^2=a c ,` prove that `y=(2x z)/(x+z)`

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Let `a^x=b^y=c^z=k`
So, `a=k^(1/x)`
`b=k^(1/y)`
`c=k^(1/z)`
Given: `b^2=ac`
`k^(2/y)=k^(1/x)k^(1/z)`
`k^(2/y)=k^(1/x+1/z)`
`2/y=1/x+1/z`
`2/y=(z+x)/(xz)`
`y=(2xz)/(z+x)`
Hence Proved.
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