Nerovnice s parametrem
Řeš s neznámou \( x \in \mathbb{ℝ} \) a s parametrem \( p\in \mathbb{ℝ} \) nerovnice:
\( \large p-x^ {2} \gt x-p^{2} \)
\( p =\ – \frac{1}{4} \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ – \frac{1}{4}} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { – \frac{1}{4};\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |
\( p =\ – \frac{2}{3} \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ – \frac{2}{3}} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { – \frac{2}{3};\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |
\( p =\ – \frac{1}{3} \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ – \frac{1}{3}} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { – \frac{1}{3};\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |
\( p =\ – \frac{1}{2} \) | \( K = ∅ \) |
\( p \in \left( { – \infty;\ – \frac{1}{2}} \right) \) | \( K = (p;\ –1\ –\ p) \) |
\( p \in \left( { – \frac{1}{2};\ \infty } \right) \) | \( K = (–1\ –\ p;\ p) \) |