Đáp án:
$\begin{array}{l}
a)A = \left( { - 7} \right) + {\left( { - 7} \right)^2} + {\left( { - 7} \right)^3} + ... + {\left( { - 7} \right)^{2019}}\\
= - 7\left( {1 - 7 + {7^2}} \right) - {7^4}\left( {1 - 7 + {7^2}} \right) - ... - {7^{2017}}\left( {1 - 7 + {7^2}} \right)\\
= - 7.43 - {7^4}.43 - ... - {7^{2017}}.43\\
= 43.\left( { - 7 - {7^4} - ... - {7^{2017}}} \right) \vdots 43\\
b)\frac{{3{a^2} - {b^2}}}{{{a^2} + {b^2}}} = \frac{3}{4}\\
\Rightarrow 4\left( {3{a^2} - {b^2}} \right) = 3\left( {{a^2} + {b^2}} \right)\\
\Rightarrow 12{a^2} - 4{b^2} = 3{a^2} + 3{b^2}\\
\Rightarrow 9{a^2} = 7{b^2}\\
\Rightarrow \frac{{{a^2}}}{{{b^2}}} = \frac{7}{9}\\
\Rightarrow \frac{a}{b} = \pm \sqrt {\frac{7}{9}} = \pm \frac{{\sqrt 7 }}{3}
\end{array}$
