(m-1)x^2-4m(m+1)x-m=0 حل کریں

$$( m - 1 ) x ^ { 2 } - 4 m ( m + 1 ) x - m = 0$$

m کے لئے حل کریں (complex solution)

$$\left\{\begin{matrix}m=-\frac{\sqrt{\left(x-1\right)\left(x^{3}-23x^{2}-9x-1\right)}-x^{2}+4x+1}{8x}\text{; }m=-\frac{-\sqrt{\left(x-1\right)\left(x^{3}-23x^{2}-9x-1\right)}-x^{2}+4x+1}{8x}\text{, }&x\neq 0\\m=0\text{, }&x=0\end{matrix}\right.$$

x کے لئے حل کریں (complex solution)

$$\left\{\begin{matrix}x=\frac{\sqrt{m\left(4m\left(m+1\right)^{2}+m-1\right)}+2m^{2}+2m}{m-1}\text{; }x=\frac{-\sqrt{m\left(4m\left(m+1\right)^{2}+m-1\right)}+2m^{2}+2m}{m-1}\text{, }&m\neq 1\\x=-\frac{1}{8}\text{, }&m=1\end{matrix}\right.$$

m کے لئے حل کریں

$$\left\{\begin{matrix}m=-\frac{\sqrt{\left(x-1\right)\left(x^{3}-23x^{2}-9x-1\right)}-x^{2}+4x+1}{8x}\text{; }m=-\frac{-\sqrt{\left(x-1\right)\left(x^{3}-23x^{2}-9x-1\right)}-x^{2}+4x+1}{8x}\text{, }&x\neq 0\text{ and }x^{4}-24x^{3}+14x^{2}+8x+1\geq 0\\m=0\text{, }&x=0\end{matrix}\right.$$

x کے لئے حل کریں

$$\left\{\begin{matrix}x=\frac{\sqrt{m\left(4m^{3}+8m^{2}+5m-1\right)}+2m^{2}+2m}{m-1}\text{; }x=\frac{-\sqrt{m\left(4m^{3}+8m^{2}+5m-1\right)}+2m^{2}+2m}{m-1}\text{, }&m\neq 1\text{ and }4m^{4}+8m^{3}+5m^{2}-m\geq 0\\x=-\frac{1}{8}\text{, }&m=1\end{matrix}\right.$$