Whakaoti mō f (complex solution)
\left\{\begin{matrix}f=\frac{\left(x-\alpha \right)\left(x-\beta \right)}{x}\text{, }&x\neq 0\\f\in \mathrm{C}\text{, }&\left(\alpha =0\text{ or }\beta =0\right)\text{ and }x=0\end{matrix}\right.
Whakaoti mō f
\left\{\begin{matrix}f=\frac{\left(x-\alpha \right)\left(x-\beta \right)}{x}\text{, }&x\neq 0\\f\in \mathrm{R}\text{, }&\left(\alpha =0\text{ or }\beta =0\right)\text{ and }x=0\end{matrix}\right.
Whakaoti mō x (complex solution)
x=\frac{-\sqrt{f^{2}+2f\alpha +2f\beta +\alpha ^{2}-2\alpha \beta +\beta ^{2}}+f+\alpha +\beta }{2}
x=\frac{\sqrt{f^{2}+2f\alpha +2f\beta +\alpha ^{2}-2\alpha \beta +\beta ^{2}}+f+\alpha +\beta }{2}
Whakaoti mō x
x=\frac{-\sqrt{f^{2}+2f\alpha +2f\beta +\alpha ^{2}-2\alpha \beta +\beta ^{2}}+f+\alpha +\beta }{2}
x=\frac{\sqrt{f^{2}+2f\alpha +2f\beta +\alpha ^{2}-2\alpha \beta +\beta ^{2}}+f+\alpha +\beta }{2}\text{, }\left(\alpha >0\text{ and }\beta <0\right)\text{ or }\left(\beta >0\text{ and }\alpha <0\right)\text{ or }f\geq 2\sqrt{\alpha \beta }-\alpha -\beta \text{ or }f\leq -2\sqrt{\alpha \beta }-\alpha -\beta \text{ or }\left(\beta \geq 0\text{ and }\alpha \leq 0\right)\text{ or }\left(\alpha \geq 0\text{ and }\beta \leq 0\right)
Graph
Tohaina
Kua tāruatia ki te papatopenga
fx=x^{2}-x\beta -\alpha x+\beta \alpha
Whakamahia te āhuatanga tohatoha hei whakarea te x-\alpha ki te x-\beta .
xf=x^{2}-x\alpha -x\beta +\alpha \beta
He hanga arowhānui tō te whārite.
\frac{xf}{x}=\frac{\left(x-\alpha \right)\left(x-\beta \right)}{x}
Whakawehea ngā taha e rua ki te x.
f=\frac{\left(x-\alpha \right)\left(x-\beta \right)}{x}
Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.
fx=x^{2}-x\beta -\alpha x+\beta \alpha
Whakamahia te āhuatanga tohatoha hei whakarea te x-\alpha ki te x-\beta .
xf=x^{2}-x\alpha -x\beta +\alpha \beta
He hanga arowhānui tō te whārite.
\frac{xf}{x}=\frac{\left(x-\alpha \right)\left(x-\beta \right)}{x}
Whakawehea ngā taha e rua ki te x.
f=\frac{\left(x-\alpha \right)\left(x-\beta \right)}{x}
Mā te whakawehe ki te x ka wetekia te whakareanga ki te x.
Ngā Tauira
whārite tapawhā
{ x } ^ { 2 } - 4 x - 5 = 0
Āhuahanga
4 \sin \theta \cos \theta = 2 \sin \theta
whārite paerangi
y = 3x + 4
Arithmetic
699 * 533
Poukapa
\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]
whārite Simultaneous
\left. \begin{cases} { 8x+2y = 46 } \\ { 7x+3y = 47 } \end{cases} \right.
Whakarerekētanga
\frac { d } { d x } \frac { ( 3 x ^ { 2 } - 2 ) } { ( x - 5 ) }
Whakaurunga
\int _ { 0 } ^ { 1 } x e ^ { - x ^ { 2 } } d x
Ngā Tepe
\lim _{x \rightarrow-3} \frac{x^{2}-9}{x^{2}+2 x-3}