3a+p/ab=2b పరిష్కరించండి

$$3 a + \frac { p } { a b } = 2 b$$

aని పరిష్కరించండి (సంకీర్ణ పరిష్కారం)

$$\left\{\begin{matrix}a=-\frac{\sqrt{b^{4}-3bp}}{3b}+\frac{b}{3}\text{, }&\left(arg(b^{2})\geq \pi \text{ or }p\neq 0\right)\text{ and }b\neq 0\\a=\frac{\sqrt{b^{4}-3bp}}{3b}+\frac{b}{3}\text{, }&b\neq 0\end{matrix}\right.$$

bని పరిష్కరించండి (సంకీర్ణ పరిష్కారం)

$$\left\{\begin{matrix}b=\frac{\sqrt{8ap+9a^{4}}}{4a}+\frac{3a}{4}\text{, }&|arg(a^{2})-arg(-\sqrt{a^{4}})|\geq \pi \text{ or }\left(p\neq 0\text{ and }a\neq 0\right)\\b=-\frac{\sqrt{8ap+9a^{4}}}{4a}+\frac{3a}{4}\text{, }&\left(|-\frac{arg(a^{4})}{2}+arg(a^{2})|\geq \pi \text{ or }p\neq 0\right)\text{ and }a\neq 0\end{matrix}\right.$$

aని పరిష్కరించండి

$$\left\{\begin{matrix}a=-\frac{\sqrt{b^{4}-3bp}}{3b}+\frac{b}{3}\text{, }&\left(p\neq 0\text{ and }p\leq \frac{b^{3}}{3}\text{ and }b>0\right)\text{ or }\left(p\neq 0\text{ and }p\geq \frac{b^{3}}{3}\text{ and }b<0\right)\text{ or }\left(b\neq 0\text{ and }p=\frac{b^{3}}{3}\right)\\a=\frac{\sqrt{b^{4}-3bp}}{3b}+\frac{b}{3}\text{, }&\left(b>0\text{ and }p<\frac{b^{3}}{3}\right)\text{ or }\left(p>\frac{b^{3}}{3}\text{ and }b<0\right)\end{matrix}\right.$$

bని పరిష్కరించండి

$$\left\{\begin{matrix}b=\frac{\sqrt{8ap+9a^{4}}}{4a}+\frac{3a}{4}\text{, }&\left(a<0\text{ or }a\geq -\frac{2\times 9^{\frac{2}{3}}\sqrt[3]{p}}{9}\right)\text{ and }\left(a>0\text{ or }a\leq -\frac{2\times 9^{\frac{2}{3}}\sqrt[3]{p}}{9}\right)\text{ and }a\neq 0\\b=-\frac{\sqrt{8ap+9a^{4}}}{4a}+\frac{3a}{4}\text{, }&p\neq 0\text{ and }\left(a<0\text{ or }a\geq -\frac{2\times 9^{\frac{2}{3}}\sqrt[3]{p}}{9}\right)\text{ and }\left(a>0\text{ or }a\leq -\frac{2\times 9^{\frac{2}{3}}\sqrt[3]{p}}{9}\right)\text{ and }a\neq 0\end{matrix}\right.$$