Řešení nerovnice v reálných číslech
Řeš v \(\mathbb{R}\) nerovnice:
\( \large \sqrt {x + 1} + \sqrt {x-2} \ge \sqrt {2-x} \)
\( \sqrt {x + 1} + \sqrt {x\ –\ 2} \ge \sqrt {2 – x} \)
\( \sqrt {3 + 1} + \sqrt {3\ –\ 2} \ge \sqrt {3\ –\ 2} \)
\( \sqrt 4 \ge 1 \)
\( \large K = \left \{ 3 \right \} \)
\( \sqrt {x + 1} + \sqrt {x\ –\ 2} \ge \sqrt {2 – x} \)
\( \sqrt {0 + 1} + \sqrt {0\ –\ 2} \ge \sqrt {0\ –\ 2} \)
\( \sqrt 1 \ge -2 \)
\( \large K = \left \{ 0 \right \} \)
\( \sqrt {x + 1} + \sqrt {x\ –\ 2} \ge \sqrt {2 – x} \)
\( \sqrt {1 + 1} + \sqrt {1\ –\ 2} \ge \sqrt {1\ –\ 2} \)
\( \sqrt 2 \ge -1 \)
\( \large K = \left \{ 1 \right \} \)
\( \sqrt {x + 1} + \sqrt {x\ –\ 2} \ge \sqrt {2 – x} \)
\( \sqrt {2 + 1} + \sqrt {2\ –\ 2} \ge \sqrt {2\ –\ 2} \)
\( \sqrt 3 \ge 0 \)
\( \large K = \left \{ 2 \right \} \)