Question

Why is geometric mean of two positive numbers a abd b is √ab not +-√ab?

Answer 1

Hey dear,

# Given-

A = 2G

# To prove-

a/b = 7 + 4√3

# Proof-

We have

A = 2G

Putting respective formulas,

(a + b) / 2 = √(ab)

(a + b) / (√ab) = 2

√(a/b) + √(b/a) = 2

Let a/b = x

√k + 1/√k = 2

Squaring both sides,

k + 1/k + 2 = 16

k^2 - 14k + 1 = 0

Solving this eqn,

k = 7 + 4√3 or k = 7 +- 4√3

a/b = 7 + 4√3 or a/b = 7 - 4√3

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