Giải thích các bước giải:
Áp dụng định lí Vi - ét ta có:
\(\left\{ \begin{array}{l}
{x_1} + {x_2} = - 1\\
{x_1}.{x_2} = - 7
\end{array} \right.\)
\(\begin{array}{l}
a,\,\,\,\,{x_1} + {x_2} = - 1\\
b,\,\,\,\,{x_1}.{x_2} = - 7\\
c,\\
{x_1}^2 + {x_2}^2 = \left( {{x_1}^2 + 2{x_1}{x_2} + {x_2}^2} \right) - 2{x_1}{x_2}\\
= {\left( {{x_1} + {x_2}} \right)^2} - 2{x_1}{x_2} = {\left( { - 1} \right)^2} - 2.\left( { - 7} \right) = 15\\
d,\\
{x_1}^3 + {x_2}^3 - {x_1} - {x_2} = \left( {{x_1} + {x_2}} \right)\left( {{x_1}^2 - {x_1}{x_2} + {x_2}^2} \right) - \left( {{x_1} + {x_2}} \right)\\
= \left( { - 1} \right).\left( {15 + 7} \right) - \left( { - 1} \right)\\
= - 22 + 1 = - 21
\end{array}\)
