解決(9+4m^2)x^2+(m^2-m)32x+(64m^2+38)=0 |Microsoft數學求解器

$$( 9 + 4 m ^ { 2 } ) x ^ { 2 } + ( m ^ { 2 } - m ) 32 x + ( 64 m ^ { 2 } + 38 ) = 0$$

解 m (復數求解)

$$\left\{\begin{matrix}m=\frac{\sqrt{-9x^{4}-72x^{3}-118x^{2}-304x-608}+8x}{2\left(x+4\right)^{2}}\text{; }m=\frac{-\sqrt{-9x^{4}-72x^{3}-118x^{2}-304x-608}+8x}{2\left(x+4\right)^{2}}\text{, }&x\neq -4\\m=-\frac{91}{64}=-1.421875\text{, }&x=-4\end{matrix}\right.$$

解 x (復數求解)

$$\left\{\begin{matrix}x=\frac{-16m^{2}+\sqrt{2\left(-256m^{3}-236m^{2}-171\right)}+16m}{4m^{2}+9}\text{; }x=\frac{-16m^{2}-\sqrt{2\left(-256m^{3}-236m^{2}-171\right)}+16m}{4m^{2}+9}\text{, }&m\neq -\frac{3}{2}i\text{ and }m\neq \frac{3}{2}i\\x=-\frac{32m^{2}+19}{16m\left(m-1\right)}\text{, }&m=-\frac{3}{2}i\text{ or }m=\frac{3}{2}i\end{matrix}\right.$$

解 m

$$\left\{\begin{matrix}m=\frac{\sqrt{-9x^{4}-72x^{3}-118x^{2}-304x-608}+8x}{2\left(x+4\right)^{2}}\text{; }m=\frac{-\sqrt{-9x^{4}-72x^{3}-118x^{2}-304x-608}+8x}{2\left(x+4\right)^{2}}\text{, }&x\neq -4\text{ and }-9x^{4}-72x^{3}-118x^{2}-304x-608\geq 0\\m=-\frac{91}{64}=-1.421875\text{, }&x=-4\end{matrix}\right.$$

解 x

$$x=\frac{-16m^{2}+\sqrt{2\left(-256m^{3}-236m^{2}-171\right)}+16m}{4m^{2}+9}$$

$$x=\frac{-16m^{2}-\sqrt{2\left(-256m^{3}-236m^{2}-171\right)}+16m}{4m^{2}+9}\text{, }-2048m^{3}-1888m^{2}-1368\geq 0$$