Verified answer

Решим системой.

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[tex] \large \begin{cases} b_1 + b_2 + b_3=26\\ b_4 + b_5 +b_6 = 702 \end{cases}[/tex]

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[tex] \large \begin{cases} b_1 + b_1 \: q + b_1 \: {q}^{2} =26 \\b_1 \: q {}^{3} + b_1 \: {q}^{4} +b_1 \: {q}^{5} =702 \end{cases}[/tex]

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[tex]\underset{ \Large \frac{ \not b_1 \: q {}^{3} ( \not 1 + \not q + \not {q }^{2}) }{ \: \: \: \: \: \not b_1( \not1 + \not q + \not{q }^{2}) } = \frac{ 702}{26} }{\underbrace{\large \begin{cases} b_1(1 + q + {q }^{2}) = 26 \\b_1 \: q {}^{3} (1 + q + {q}^{2} ) = 702\end{cases}}} \\ [/tex]

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[tex] \: \: \large {q}^{3} = \frac{702}{26} \\ \\\large {q}^{3} =27 \: \:\\ \\ \large q = \sqrt[3]{27} \\ \\ \large q = 3\: \: \: \: \: \: [/tex]

⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀⠀Ответ: q=3