{l}{6x^{2}+(b-2a)x=b^{2}+ab}{(a^{2}-b^2)x^2-4abx+b^2=a^2} ಪರಿಹರಿಸಿ

$$\left. \begin{array} { l } { 6 x ^ { 2 } + ( b - 2 a ) x = b ^ { 2 } + a b } \\ { ( a ^ { 2 } - b ^ { 2 } ) x ^ { 2 } - 4 a b x + b ^ { 2 } = a ^ { 2 } } \end{array} \right.$$

x ಪರಿಹರಿಸಿ (ಸಂಕೀರ್ಣ ಪರಿಹಾರ)

$$\left\{\begin{matrix}x=\frac{a+b}{3}\text{, }&b=-a\text{ or }b=-a+\frac{\sqrt{9-24a}}{2}+\frac{3}{2}\text{ or }b=-a-\frac{\sqrt{9-24a}}{2}+\frac{3}{2}\text{ or }b=a-3\\x=-\frac{b}{2}\text{, }&b=-\sqrt{-\frac{\sqrt{\left(a+2\right)^{2}\left(a^{2}+12a+4\right)}}{2}+\frac{a^{2}}{2}+4a+2}\text{ or }b=\sqrt{-\frac{\sqrt{\left(a+2\right)^{2}\left(a^{2}+12a+4\right)}}{2}+\frac{a^{2}}{2}+4a+2}\text{ or }b=-\sqrt{\frac{\sqrt{\left(a+2\right)^{2}\left(a^{2}+12a+4\right)}}{2}+\frac{a^{2}}{2}+4a+2}\text{ or }b=\sqrt{\frac{\sqrt{\left(a+2\right)^{2}\left(a^{2}+12a+4\right)}}{2}+\frac{a^{2}}{2}+4a+2}\end{matrix}\right.$$