Đáp án:
$\begin{array}{l}
a)\left( {x + 4} \right) + \left( {x + 8} \right) + \left( {x + 12} \right) + ... + \left( {x + 132} \right) = 5577\\
\Rightarrow \left( {x + x + .. + x} \right) + \left( {4 + 8 + 12 + ... + 132} \right) = 5577
\end{array}$
Có số số hạng là:$\dfrac{{132 - 4}}{4} + 1 = 33$
$\begin{array}{l}
\Rightarrow 33.x + \dfrac{{\left( {132 + 4} \right).33}}{2} = 5577\\
\Rightarrow 33.x + 2244 = 5577\\
\Rightarrow 33.x = 3333\\
\Rightarrow x = 101
\end{array}$
Vậy x=101
$\begin{array}{l}
b){x^{2020}} = {x^{10}}\\
\Rightarrow {x^{2020}} - {x^{10}} = 0\\
\Rightarrow {x^{10 + 2010}} - {x^{10}} = 0\\
\Rightarrow {x^{10}}.{x^{2010}} - {x^{10}} = 0\\
\Rightarrow {x^{10}}.\left( {{x^{2010}} - 1} \right) = 0\\
\Rightarrow \left[ \begin{array}{l}
{x^{10}} = 0\\
{x^{2010}} = 1
\end{array} \right.\\
\Rightarrow \left[ \begin{array}{l}
x = 0\\
x = 1\\
x = - 1
\end{array} \right.
\end{array}$
Vậy x=0;x=1;x=-1
$\begin{array}{l}
c){3^{x + 2}} + {3^x} = 2430\\
\Rightarrow {3^x}{.3^2} + {3^x} = 2430\\
\Rightarrow {3^x}.\left( {{3^2} + 1} \right) = 2430\\
\Rightarrow {3^x}.10 = 2430\\
\Rightarrow {3^x} = 243\\
\Rightarrow {3^x} = {3^5}\\
\Rightarrow x = 5
\end{array}$
Vậy x=5
