If, a : b = b : c then a4 : b4 would be equal to: 1. ac : b2 2. a2 : c2 3. b2 : ac 4. c2 : a2

Given, a : b = b : c ⇒ b2 = ac ⇒ b4 = (ac)2 ⇒ b4 = a2c2. ⇒ a4 : b4 = a2 : c2 Hence, option 2 is the correct option.

Mathematics

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Given,

a : b = b : c

$\Rightarrow \dfrac{a}{b} = \dfrac{b}{c}$

⇒ b² = ac

⇒ b⁴ = (ac)²

⇒ b⁴ = a²c².

$\Rightarrow \dfrac{a^4}{b^4} = \dfrac{a^4}{a^2c^2} \\[1em] = \dfrac{a^4}{a^2c^2} \\[1em] = \dfrac{a^{4 - 2}}{c^2} \\[1em] = \dfrac{a^{2}}{c^2}.$

⇒ a⁴ : b⁴ = a² : c²

Hence, option 2 is the correct option.

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