Question

If a^x = b^y = c^z and b² = ac, show that `y=(2zx)/(z+x)`

Answer 1

Let a^x = b^y = c^z = 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)`