Riešenie nerovnice s parametrom
Rieš s neznámou x \( \in\:\R \) a s parametrom p \( \in\:\R \) nerovnice:
\( \large p-x^ {2} \gt x-p^{2} \)
\( p =\ 1 \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ 1} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { 1;\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |
\( p =\ 0 \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ 0} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { 0;\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |
\( p =\ – \frac{1}{2} \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ – \frac{1}{2}} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { – \frac{1}{2};\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |
\( p =\ – \frac{3}{2} \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ – \frac{3}{2}} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { – \frac{3}{2};\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |