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If a : b = b : c, then a⁴ : b⁴ is equal to = ?

1ac = b²
2a² : c²
3c² : a²
4b² : ac

Answer:- 1

Explanation:-

Solution:

\begin{aligned} a : b = b : c \\ \frac{a}{b} = \frac{b}{c} \\ b^{2} = a c \\ b^{4} = a^{2} c^{2} \\ ∴ a^{4} : b^{4} = \frac{a^{4}}{b^{4}} \\ = \frac{a^{4}}{a^{2} c^{2}} \\ = \frac{a^{2}}{c^{2}} \\ = a^{2} : c^{2} \end{aligned}

$\eqalign{ & a:b = b:c \cr & \frac{a}{b} = \frac{b}{c} \cr & {b^2} = ac \cr & {b^4} = {a^2}{c^2} \cr & \therefore {a^4}:{b^4} = \frac{{{a^4}}}{{{b^4}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^4}}}{{{a^2}{c^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^2}}}{{{c^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {a^2}:{c^2} \cr}$

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", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} a : b = b : c \\ \frac{a}{b} = \frac{b}{c} \\ b^{2} = a c \\ b^{4} = a^{2} c^{2} \\ ∴ a^{4} : b^{4} = \frac{a^{4}}{b^{4}} \\ = \frac{a^{4}}{a^{2} c^{2}} \\ = \frac{a^{2}}{c^{2}} \\ = a^{2} : c^{2} \end{aligned}

$\eqalign{ & a:b = b:c \cr & \frac{a}{b} = \frac{b}{c} \cr & {b^2} = ac \cr & {b^4} = {a^2}{c^2} \cr & \therefore {a^4}:{b^4} = \frac{{{a^4}}}{{{b^4}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^4}}}{{{a^2}{c^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = \frac{{{a^2}}}{{{c^2}}} \cr & \,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\,\, = {a^2}:{c^2} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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