\left\{ \begin{array} { l } { A ^ { 2 } + B ^ { 2 } = L B } \\ { 2 A + B = 3 X } \end{array} \right.
Resolver A, B, L, X (complex solution)
A=\frac{3X-B}{2}\text{, }B=\frac{2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{C}\text{, }X\in \mathrm{C}
A=\frac{3X-B}{2}\text{, }B=\frac{-2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{C}\text{, }X\in \mathrm{C}
Resolver A, B, L, X
\left\{\begin{matrix}A=\frac{3X-B}{2}\text{, }B=\frac{2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\in \begin{bmatrix}\frac{\sqrt{5}L+L}{6},\frac{-\sqrt{5}L+L}{6}\end{bmatrix}\text{; }A=\frac{3X-B}{2}\text{, }B=\frac{-2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\in \begin{bmatrix}\frac{\sqrt{5}L+L}{6},\frac{-\sqrt{5}L+L}{6}\end{bmatrix}\text{, }&L\leq 0\\A=\frac{3X-B}{2}\text{, }B=\frac{2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\geq \frac{\sqrt{5}L+L}{6}\text{; }A=\frac{3X-B}{2}\text{, }B=\frac{-2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\geq \frac{\sqrt{5}L+L}{6}\text{, }&L>0\\A=\frac{3X-B}{2}\text{, }B=\frac{2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\in \mathrm{R}\text{; }A=\frac{3X-B}{2}\text{, }B=\frac{-2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\in \mathrm{R}\text{, }&L\neq 0\\A=\frac{3X-B}{2}\text{, }B=\frac{2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\in \begin{bmatrix}\frac{-\sqrt{5}L+L}{6},\frac{\sqrt{5}L+L}{6}\end{bmatrix}\text{; }A=\frac{3X-B}{2}\text{, }B=\frac{-2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\in \begin{bmatrix}\frac{-\sqrt{5}L+L}{6},\frac{\sqrt{5}L+L}{6}\end{bmatrix}\text{, }&L\geq 0\\A=\frac{3X-B}{2}\text{, }B=\frac{2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\geq \frac{-\sqrt{5}L+L}{6}\text{; }A=\frac{3X-B}{2}\text{, }B=\frac{-2\sqrt{L^{2}+3LX-9X^{2}}+2L+3X}{5}\text{, }L\in \mathrm{R}\text{, }X\geq \frac{-\sqrt{5}L+L}{6}\text{, }&L<0\end{matrix}\right.
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Exemplos
Ecuación cuadrática
{ x } ^ { 2 } - 4 x - 5 = 0
Trigonometría
4 \sin \theta \cos \theta = 2 \sin \theta
Ecuación linear
y = 3x + 4
Aritmética
699 * 533
Matriz
\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]
Ecuación simultánea
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Diferenciación
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Integración
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Límites
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}