Rovnica s neznámou a parametrom
Rieš s neznámou \( x \in \mathbb{ℝ} \) a s parametrom \( r\in\mathbb{R} \) rovnicu:
\( \large\frac{x}{{x+r}}+\frac{{2x}}{{x-r}}=\frac{{5r^2}}{{4\left({x^2-r^2}\right)}} \)
parameter | riešenie pre x |
\( r = 0 \) | \( K = \{0\} \) |
\( r \in \left( { – \infty;\ 0} \right)\mathop \cup \nolimits \left( {0;\ \infty } \right) \) | \( K=\left \{ –\frac{3r}{4};\ \frac{r}{3} \right \} \) |
parameter | riešenie pre x |
\( r = 0 \) | \( K = \emptyset \) |
\( r \in \left( { – \infty;\ 0} \right)\mathop \cup \nolimits \left( {0;\ \infty } \right) \) | \( K=\left \{ –\frac{5r}{6};\ \frac{r}{2} \right \} \) |
parameter | riešenie pre x |
\( r = 0 \) | \( K = \{x \in \mathbb{R}\} \) |
\( r \in \left( { – \infty;\ 0} \right)\mathop \cup \nolimits \left( {0;\ \infty } \right) \) | \( K=\left \{ –\frac{4r}{5};\ \frac{r}{4} \right \} \) |
parameter | riešenie pre x |
\( r = 0 \) | \( K = \{1\} \) |
\( r \in \left( { – \infty;\ 0} \right)\mathop \cup \nolimits \left( {0;\ \infty } \right) \) | \( K=\left \{ –\frac{6r}{7};\ \frac{r}{5} \right \} \) |