Question

Determine o valor de

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Answer 1

Resposta:

Leia abaixo

Explicação passo-a-passo:

$\dfrac{c}{a + 3b} =\dfrac{a}{b + 3c} \iff a^2 + 3ab = bc + 3c^2 \iff a^2 = bc + 3c^2 - 3ab$

$\dfrac{a}{b + 3c} =\dfrac{b}{c + 3a} \iff b^2 + 3bc = ac + 3a^2$

$\dfrac{c}{a + 3b} =\dfrac{b}{c + 3a} \iff = c^2 + 3ac = ab + 3b^2$

$b^2 + 3bc = ac + 3bc + 9c^2 - 9ab \iff b^2 = ac + 9c^2 - 9ab$

$c^2 + 3ac = ab + 3ac + 27c^2 - 27ab \iff 26c^2 = 26ab \iff c^2 = ab$

$\begin{cases}a^2 = bc\\b^2 = ac\\c^2 = ab\end{cases}$

$\dfrac{a^2}{b} = \dfrac{b^2}{a} \iff a^3 = b^3$

$\dfrac{b^2}{c} = \dfrac{c^2}{b} \iff b^3 = c^3$

$\boxed{\boxed{a = b = c}}$