Løs for x
\left\{\begin{matrix}x\neq 15\text{, }&k=4\\x\neq 7\text{, }&k=2\\x\in \mathrm{R}\text{, }&k>2\text{ and }k<4\\x\in \left(\sqrt{\left(k-4\right)\left(k-2\right)}+4k-1,\infty\right)\cup \left(-\infty,-\sqrt{\left(k-4\right)\left(k-2\right)}+4k-1\right)\text{, }&k<2\text{ or }k>4\end{matrix}\right,
Løs for k
\left\{\begin{matrix}k\neq -\frac{4\sqrt{15}}{15}+3\text{, }&x=11-\sqrt{15}\\k\neq \frac{4\sqrt{15}}{15}+3\text{, }&x=\sqrt{15}+11\\k\in \mathrm{R}\text{, }&x>11-\sqrt{15}\text{ and }x<\sqrt{15}+11\\k\in \left(\frac{\sqrt{x^{2}-22x+106}+4x+1}{15},\infty\right)\cup \left(-\infty,\frac{-\sqrt{x^{2}-22x+106}+4x+1}{15}\right)\text{, }&x<11-\sqrt{15}\text{ or }x>\sqrt{15}+11\end{matrix}\right,
Graf
Aktie
Kopieret til udklipsholder
Eksempler
Kvadratisk ligning
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometri
4 \sin \theta \cos \theta = 2 \sin \theta
Lineær ligning
y = 3x + 4
Aritmetik
699 * 533
Matrix
\left[ \begin{array} { l l } { 2 } & { 3 } \\ { 5 } & { 4 } \end{array} \right] \left[ \begin{array} { l l l } { 2 } & { 0 } & { 3 } \\ { -1 } & { 1 } & { 5 } \end{array} \right]
Samtidig ligning
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Differentiering
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integration
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Grænser
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}