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

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

برای x حل کنید (complex solution)

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

برای x حل کنید

$$\left\{\begin{matrix}x=\frac{a+b}{3}\text{, }&b=-a\text{ or }\left(b=-a+\frac{\sqrt{9-24a}}{2}+\frac{3}{2}\text{ and }a\leq \frac{3}{8}\right)\text{ or }\left(b=-a-\frac{\sqrt{9-24a}}{2}+\frac{3}{2}\text{ and }a\leq \frac{3}{8}\right)\text{ or }b=a-3\\x=-\frac{b}{2}\text{, }&\left(a\leq -4\sqrt{2}-6\text{ and }2a\sqrt{a^{2}+12a+4}+2a^{2}+4\sqrt{a^{2}+12a+4}+16a\geq -8\text{ and }|b|=\frac{\sqrt{2a\sqrt{a^{2}+12a+4}+2a^{2}+4\sqrt{a^{2}+12a+4}+16a+8}}{2}\right)\text{ or }\left(a\geq 4\sqrt{2}-6\text{ and }2a\sqrt{a^{2}+12a+4}+2a^{2}+4\sqrt{a^{2}+12a+4}+16a\geq -8\text{ and }|b|=\frac{\sqrt{2a\sqrt{a^{2}+12a+4}+2a^{2}+4\sqrt{a^{2}+12a+4}+16a+8}}{2}\right)\text{ or }\left(a=4\sqrt{2}-6\text{ and }|b|=2\sqrt{2}-2\right)\text{ or }\left(a=-4\sqrt{2}-6\text{ and }|b|=2\sqrt{2}+2\right)\text{ or }\left(a\leq -4\sqrt{2}-6\text{ and }-2a\sqrt{a^{2}+12a+4}+2a^{2}-4\sqrt{a^{2}+12a+4}+16a\geq -8\text{ and }|b|=\frac{\sqrt{-2a\sqrt{a^{2}+12a+4}+2a^{2}-4\sqrt{a^{2}+12a+4}+16a+8}}{2}\right)\text{ or }\left(a\geq 4\sqrt{2}-6\text{ and }-2a\sqrt{a^{2}+12a+4}+2a^{2}-4\sqrt{a^{2}+12a+4}+16a\geq -8\text{ and }|b|=\frac{\sqrt{-2a\sqrt{a^{2}+12a+4}+2a^{2}-4\sqrt{a^{2}+12a+4}+16a+8}}{2}\right)\end{matrix}\right.$$