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Question
If ax = by = cz and b2 = ac, show that `y=(2zx)/(z+x)`
Solution
Let ax = by = cz = k
So, `a=k^(1/x),` `b=k^(1/y),` c=k^(1/z)
Thus,
`b^2 = ac`
`rArr(k^(1/y))^2=(k^(1/x))(k^(1/z))`
`rArrk^(2/y)=k^(1/x+1/z)`
`rArr2/y=1/x+1/z`
`rArr2/y=(z+x)/(xz)`
`rArr2xx(zx)/(z+x)=y`
`rArry=(2zx)/(z+x)`
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