Giải thích các bước giải:
Ta có:
\(\begin{array}{l}
1,\\
{83^2} + 34.83 + {17^2}\\
= {83^2} + 2.83.17 + {17^2}\\
= {\left( {83 + 17} \right)^2}\\
= {100^2}\\
= 10000\\
2,\\
a,\\
{x^2} - 25 = {x^2} - {5^2} = \left( {x - 5} \right)\left( {x + 5} \right)\\
b,\\
{x^2} - xy + x = x.\left( {x - y + 1} \right)\\
c,\\
{x^2} + 2{x^2}y + x{y^2} - 4x\\
= x.\left( {x + 2xy + {y^2} - 4} \right)\\
d,\\
4 - {x^2} - 2xy - {y^2}\\
= 4 - \left( {{x^2} + 2xy + {y^2}} \right)\\
= 4 - {\left( {x + y} \right)^2}\\
= {2^2} - {\left( {x + y} \right)^2}\\
= \left[ {2 - \left( {x + y} \right)} \right].\left[ {2 + \left( {x + y} \right)} \right]\\
= \left( {2 - x - y} \right)\left( {2 + x + y} \right)\\
3,\\
a,\\
{\left( {x - 2} \right)^2} - 5x + 10 = 0\\
\Leftrightarrow {\left( {x - 2} \right)^2} - \left( {5x - 10} \right) = 0\\
\Leftrightarrow {\left( {x - 2} \right)^2} - 5.\left( {x - 2} \right) = 0\\
\Leftrightarrow \left( {x - 2} \right)\left[ {\left( {x - 2} \right) - 5} \right] = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {x - 7} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 2 = 0\\
x - 7 = 0
\end{array} \right.\\
\Leftrightarrow \left[ \begin{array}{l}
x = 2\\
x = 7
\end{array} \right.\\
b,\\
{\left( {2x - 3} \right)^2} - {\left( {x - 1} \right)^2} = 0\\
\Leftrightarrow \left[ {\left( {2x - 3} \right) - \left( {x - 1} \right)} \right].\left[ {\left( {2x - 3} \right) + \left( {x - 1} \right)} \right] = 0\\
\Leftrightarrow \left( {x - 2} \right)\left( {3x - 4} \right) = 0\\
\Leftrightarrow \left[ \begin{array}{l}
x - 2 = 0\\
3x - 4 = 0
\end{array} \right. \Leftrightarrow \left[ \begin{array}{l}
x = 2\\
x = \dfrac{4}{3}
\end{array} \right.
\end{array}\)
