Question

If a^x =b^y =c^z , and b^2=ac then prove that 1/x +1/z =2/y

[Please show the steps and don't use logarithm]

Thanks :)

Answer 1

Given ax = by = cz and b2 = ac
Let ax = by = cz = k
Consider,  ax = k  ⇒ a = k1/x
Similarly, we get b = k1/y and c = k1/z
Now consider, b2 = ac
⇒ (k1/y)2 = (k1/x)(k1/z)
⇒ k2/y =  k1/x + 1/z
Comparing both the sides, we get
(2/y) = (1/x) + (1/z)
⇒ (2/y) = (x + z)/xz
∴ y = (2xz)/(x + z)

Answer 2

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