(0^2-D)^y=x सोडवा

$$( 0 ^ { 2 } - D ) ^ { y } = x$$

D साठी सोडवा (जटिल उत्तर)

$$D=e^{\frac{Im(y)arg(x)+iRe(y)arg(x)}{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}-\frac{2\pi n_{1}iRe(y)}{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}-\frac{2\pi n_{1}Im(y)}{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}}\left(|x|\right)^{\frac{Re(y)-iIm(y)}{\left(Re(y)\right)^{2}+\left(Im(y)\right)^{2}}}$$

$$n_{1}\in \mathrm{Z}$$

x साठी सोडवा (जटिल उत्तर)

$$x=\left(-D\right)^{y}$$

D साठी सोडवा

$$\left\{\begin{matrix}D=-x^{\frac{1}{y}}\text{, }&\left(Numerator(y)\text{bmod}2=1\text{ and }Denominator(y)\text{bmod}2=1\text{ and }x<0\text{ and }x^{\frac{1}{y}}\neq 0\right)\text{ or }\left(x=0\text{ and }y>0\right)\text{ or }\left(x>0\text{ and }y\neq 0\right)\\D=x^{\frac{1}{y}}\text{, }&\left(x<0\text{ and }Numerator(y)\text{bmod}2=1\text{ and }Numerator(y)\text{bmod}2=0\text{ and }Denominator(y)\text{bmod}2=1\text{ and }x^{\frac{1}{y}}\neq 0\right)\text{ or }\left(y\neq 0\text{ and }x>0\text{ and }Numerator(y)\text{bmod}2=0\text{ and }Denominator(y)\text{bmod}2=1\right)\text{ or }\left(Numerator(y)\text{bmod}2=0\text{ and }x=0\text{ and }y>0\right)\text{ or }\left(x>0\text{ and }y\neq 0\text{ and }x^{\frac{1}{y}}<0\text{ and }Numerator(y)\text{bmod}2=0\right)\\D\neq 0\text{, }&y=0\text{ and }x=1\end{matrix}\right.$$

x साठी सोडवा

$$x=\left(-D\right)^{y}$$

$$\left(D>0\text{ and }Denominator(y)\text{bmod}2=1\right)\text{ or }\left(D=0\text{ and }y>0\right)\text{ or }D<0$$