Επίλυση 2003a^2+2002a-2001=02001b^2-2002b-2003=011abneq1

$$2003 a ^ { 2 } + 2002 a - 2001 = 02001 b ^ { 2 } - 2002 b - 2003 = 011 a b \neq 1$$

Υπολογισμός (complex solution)

$$2003a^{2}+2002a-2001=2001b^{2}-2002b-2003\text{ and }2001b^{2}-2002b-2003=11ab\text{ and }11ab\neq 1$$

Λύση ως προς b

$$\left\{\begin{matrix}b=\frac{\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}\text{, }&\left(\frac{\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}=-\frac{\sqrt{121a^{2}+44044a+20040016}}{4002}+\frac{11a}{4002}+\frac{1001}{2001}\text{ or }\frac{\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}=\frac{\sqrt{121a^{2}+44044a+20040016}}{4002}+\frac{11a}{4002}+\frac{1001}{2001}\right)\text{ and }\frac{\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}\neq \frac{1}{11a}\\b=\frac{-\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}\text{, }&\left(\frac{-\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}=-\frac{\sqrt{121a^{2}+44044a+20040016}}{4002}+\frac{11a}{4002}+\frac{1001}{2001}\text{ or }\frac{-\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}=\frac{\sqrt{121a^{2}+44044a+20040016}}{4002}+\frac{11a}{4002}+\frac{1001}{2001}\right)\text{ and }\frac{-\sqrt{4008003a^{2}+4006002a+1006003}+1001}{2001}\neq \frac{1}{11a}\end{matrix}\right,$$

Λύση ως προς a

$$\left\{\begin{matrix}a=\frac{\sqrt{4008003b^{2}-4010006b+997995}-1001}{2003}\text{, }&\left(b\geq \frac{2\sqrt{5017519006}}{4008003}+\frac{1001}{2001}\text{ or }b\leq -\frac{2\sqrt{5017519006}}{4008003}+\frac{1001}{2001}\right)\text{ and }b\neq 0\text{ and }\frac{\sqrt{4008003b^{2}-4010006b+997995}-1001}{2003}=\frac{2001b}{11}-182-\frac{2003}{11b}\text{ and }\frac{\sqrt{4008003b^{2}-4010006b+997995}-1001}{2003}\neq \frac{1}{11b}\\a=\frac{-\sqrt{4008003b^{2}-4010006b+997995}-1001}{2003}\text{, }&\left(b\geq \frac{2\sqrt{5017519006}}{4008003}+\frac{1001}{2001}\text{ or }b\leq -\frac{2\sqrt{5017519006}}{4008003}+\frac{1001}{2001}\right)\text{ and }b\neq 0\text{ and }\frac{-\sqrt{4008003b^{2}-4010006b+997995}-1001}{2003}=\frac{2001b}{11}-182-\frac{2003}{11b}\text{ and }\frac{-\sqrt{4008003b^{2}-4010006b+997995}-1001}{2003}\neq \frac{1}{11b}\end{matrix}\right,$$