# If Ax = By = Cz And B2 = Ac, Prove That : Y = 2az/X + Z - Mathematics

Sum

If ax = by = cz and b2 = ac, prove that : y = [2az]/[x + z]

#### Solution

Let ax = by = cz = k
∴ a = k^(1/x) ; b = k^(1/y) ; c = k^(1/z)

Also, We have b2 = ac
∴ ( k^(1/y))^2 = ( k^(1/x)) xx ( k^(1/2))

⇒ k^(2/y) = k^( 1/x + 1/z )

⇒ k^(2/y) = k^[ z + x ]/[  xz ]

Comparing the powers we have
2/y = [ z + x ]/[ xz ]

⇒ y = [ 2 xz ]/[ z + x ]

Concept: Solving Exponential Equations
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#### APPEARS IN

Selina Concise Mathematics Class 9 ICSE
Chapter 7 Indices (Exponents)
Exercise 7 (B) | Q 9 | Page 100