a) Ta có: \({x^2} - 5 = 0\)
\(\Leftrightarrow {x^2} - {\left( {\sqrt 5 } \right)^2} = 0\)
\(\Leftrightarrow \left( {x + \sqrt 5 } \right).\left( {x - \sqrt 5 } \right) = 0\)
\( \Leftrightarrow \left[ \matrix{
x + \sqrt 5 = 0 \hfill \cr
x - \sqrt 5 = 0 \hfill \cr} \right.\)
\( \Leftrightarrow \left[ \matrix{
x = - \sqrt 5 \hfill \cr
x = \sqrt 5 \hfill \cr} \right.\)
Vậy \( S = \left\{ { - \sqrt 5 ;\sqrt 5 } \right\} \).
b) Ta có:
\({x^2} - 2\sqrt {11} x + 11 = 0 \)
\( \Leftrightarrow {x^2} - 2.x.\sqrt {11} + {\left( {\sqrt {11} } \right)^2} = 0 \)
\( \Leftrightarrow {\left( {x - \sqrt {11} } \right)^2} = 0 \)
\(\Leftrightarrow x - \sqrt {11} =0\)
\(\Leftrightarrow x = \sqrt {11} \)
Vậy \(S = \left\{ {\sqrt {11} } \right\} \)
