2003a^2+2002a-2001=0.2001b^2-2002b-2003=0.11abneq1 କୁ ସମାଧାନ କରନ୍ତୁ

$$2003 a ^ { 2 } + 2002 a - 2001 = 0.2001 b ^ { 2 } - 2002 b - 2003 = 0.11 a b \neq 1$$

ମୂଲ୍ୟାୟନ କରିବା (ଜଟଳି ସମାଧାନ)

$$2003a^{2}+2002a-2001=\frac{2001b^{2}}{10000}-2002b-2003\text{ and }\frac{2001b^{2}}{10000}-2002b-2003=\frac{11ab}{100}\text{ and }\frac{11ab}{100}\neq 1$$

b ପାଇଁ ସମାଧାନ କରନ୍ତୁ

$$\left\{\begin{matrix}b=\frac{5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}\text{, }&\left(\frac{5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}=\frac{-5000\sqrt{\frac{121a^{2}}{10000}+\frac{11011a}{25}+4009607.2012}+550a+10010000}{2001}\text{ or }\frac{5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}=\frac{5000\sqrt{\frac{121a^{2}}{10000}+\frac{11011a}{25}+4009607.2012}+550a+10010000}{2001}\right)\text{ and }\frac{5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}\neq \frac{100}{11a}\\b=\frac{-5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}\text{, }&\left(\frac{-5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}=\frac{-5000\sqrt{\frac{121a^{2}}{10000}+\frac{11011a}{25}+4009607.2012}+550a+10010000}{2001}\text{ or }\frac{-5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}=\frac{5000\sqrt{\frac{121a^{2}}{10000}+\frac{11011a}{25}+4009607.2012}+550a+10010000}{2001}\right)\text{ and }\frac{-5000\sqrt{\frac{4008003a^{2}}{2500}+\frac{2003001a}{1250}+4008005.6008}[phone]}{2001}\neq \frac{100}{11a}\end{matrix}\right.$$

a ପାଇଁ ସମାଧାନ କରନ୍ତୁ

$$\left\{\begin{matrix}a=\frac{\sqrt{4008003b^{2}-40100060000b+9979950000}}{200300}-\frac{1001}{2003}\text{, }&\left(b\geq \frac{100\sqrt{40196370333136015}}{4008003}+\frac{10010000}{2001}\text{ or }b\leq -\frac{100\sqrt{40196370333136015}}{4008003}+\frac{10010000}{2001}\right)\text{ and }b\neq 0\text{ and }\frac{\sqrt{4008003b^{2}-40100060000b+9979950000}}{200300}-\frac{1001}{2003}=\frac{2001b}{1100}-18200-\frac{200300}{11b}\text{ and }\frac{\sqrt{4008003b^{2}-40100060000b+9979950000}}{200300}-\frac{1001}{2003}\neq \frac{100}{11b}\\a=-\frac{\sqrt{4008003b^{2}-40100060000b+9979950000}}{200300}-\frac{1001}{2003}\text{, }&\left(b\geq \frac{100\sqrt{40196370333136015}}{4008003}+\frac{10010000}{2001}\text{ or }b\leq -\frac{100\sqrt{40196370333136015}}{4008003}+\frac{10010000}{2001}\right)\text{ and }b\neq 0\text{ and }-\frac{\sqrt{4008003b^{2}-40100060000b+9979950000}}{200300}-\frac{1001}{2003}=\frac{2001b}{1100}-18200-\frac{200300}{11b}\text{ and }-\frac{\sqrt{4008003b^{2}-40100060000b+9979950000}}{200300}-\frac{1001}{2003}\neq \frac{100}{11b}\end{matrix}\right.$$