a^ x is equal to b ^ Y is equal to C ^z and B square is equal to AC prove y= 2xz÷x+z
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Hey.
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).
Hope it helps.
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).
Hope it helps.
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