(9+lnm^2)x^2+(m^2-m)32x+(64m^2+38)=0 സോൾവ് ചെയ്യുക

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

x എന്നതിനായി സോൾവ് ചെയ്യുക (സങ്കീർണ്ണ സൊല്യൂഷൻ)

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(-32m^{2}\ln(m^{2})-19\ln(m^{2})+128m^{4}-256m^{3}-160m^{2}-171\right)}-16m^{2}+16m}{\ln(m^{2})+9}\text{; }x=\frac{-\sqrt{2\left(-32m^{2}\ln(m^{2})-19\ln(m^{2})+128m^{4}-256m^{3}-160m^{2}-171\right)}-16m^{2}+16m}{\ln(m^{2})+9}\text{, }&m\neq -\frac{1}{e^{\frac{9}{2}}}\text{ and }m\neq \frac{1}{e^{\frac{9}{2}}}\text{ and }m\neq 0\\x=-\frac{32m^{2}+19}{16m\left(m-1\right)}\text{, }&m=-\frac{1}{e^{\frac{9}{2}}}\text{ or }m=\frac{1}{e^{\frac{9}{2}}}\end{matrix}\right.$$

x എന്നതിനായി സോൾവ് ചെയ്യുക

$$\left\{\begin{matrix}x=\frac{\sqrt{2\left(-32m^{2}\ln(m^{2})-19\ln(m^{2})+128m^{4}-256m^{3}-160m^{2}-171\right)}-16m^{2}+16m}{\ln(m^{2})+9}\text{; }x=\frac{-\sqrt{2\left(-32m^{2}\ln(m^{2})-19\ln(m^{2})+128m^{4}-256m^{3}-160m^{2}-171\right)}-16m^{2}+16m}{\ln(m^{2})+9}\text{, }&m\neq 0\text{ and }-256m^{2}\ln(m^{2})-152\ln(m^{2})+1024m^{4}-2048m^{3}-1280m^{2}\geq 1368\text{ and }|m|\neq \frac{1}{e^{\frac{9}{2}}}\\x=-\frac{32m^{2}+19}{16m\left(m-1\right)}\text{, }&|m|=\frac{1}{e^{\frac{9}{2}}}\end{matrix}\right.$$