4^4-22x^4=-45x^4y^4 ಪರಿಹರಿಸಿ

$$4 ^ { 4 } - 22 x ^ { 4 } = - 45 x ^ { 4 } y ^ { 4 }$$

x ಪರಿಹರಿಸಿ (ಸಂಕೀರ್ಣ ಪರಿಹಾರ)

$$x=\sqrt{2}\left(-2+2i\right)\left(45y^{4}-22\right)^{-\frac{1}{4}}$$

$$x=\sqrt{2}\left(2+2i\right)\left(45y^{4}-22\right)^{-\frac{1}{4}}$$

$$x=\sqrt{2}\left(-2-2i\right)\left(45y^{4}-22\right)^{-\frac{1}{4}}$$

$$x=\sqrt{2}\left(2-2i\right)\left(45y^{4}-22\right)^{-\frac{1}{4}}\text{, }y\neq -\frac{45^{\frac{3}{4}}\sqrt[4]{22}i}{45}\text{ and }y\neq -\frac{45^{\frac{3}{4}}\sqrt[4]{22}}{45}\text{ and }y\neq \frac{45^{\frac{3}{4}}\sqrt[4]{22}i}{45}\text{ and }y\neq \frac{45^{\frac{3}{4}}\sqrt[4]{22}}{45}$$

y ಪರಿಹರಿಸಿ (ಸಂಕೀರ್ಣ ಪರಿಹಾರ)

$$y=\frac{45^{\frac{3}{4}}i\sqrt[4]{22-\frac{256}{x^{4}}}}{45}$$

$$y=\frac{45^{\frac{3}{4}}\sqrt[4]{22-\frac{256}{x^{4}}}}{45}$$

$$y=-\frac{45^{\frac{3}{4}}\sqrt[4]{22-\frac{256}{x^{4}}}}{45}$$

$$y=-\frac{45^{\frac{3}{4}}i\sqrt[4]{22-\frac{256}{x^{4}}}}{45}\text{, }x\neq 0$$

x ಪರಿಹರಿಸಿ

$$x=4\sqrt[4]{-\frac{1}{45y^{4}-22}}$$

$$x=-4\sqrt[4]{-\frac{1}{45y^{4}-22}}\text{, }|y|\leq \frac{45^{\frac{3}{4}}\sqrt[4]{22}}{45}\text{ and }|y|\neq \frac{\sqrt[4]{24750}}{15}$$

y ಪರಿಹರಿಸಿ

$$\left\{\begin{matrix}y=\frac{\sqrt[4]{2250}\sqrt{-\sqrt{11x^{4}-128}}}{15x}\text{; }y=-\frac{\sqrt[4]{2250}\sqrt{-\sqrt{11x^{4}-128}}}{15x}\text{, }&\left(-2\times \frac{11^{\frac{3}{4}}}{11}\sqrt[4]{8}=-\frac{2\times 22^{\frac{3}{4}}}{11}\text{ and }x=-2\times \frac{11^{\frac{3}{4}}}{11}\sqrt[4]{8}\right)\text{ or }\left(\frac{2\times 22^{\frac{3}{4}}}{11}<2\times \frac{11^{\frac{3}{4}}}{11}\sqrt[4]{8}\text{ and }x=-\frac{2\times 22^{\frac{3}{4}}}{11}\text{ and }-\frac{2\times 22^{\frac{3}{4}}}{11}\leq -2\times \frac{11^{\frac{3}{4}}}{11}\sqrt[4]{8}\right)\text{ or }\left(2\times \frac{11^{\frac{3}{4}}}{11}\sqrt[4]{8}=\frac{2\times 22^{\frac{3}{4}}}{11}\text{ and }x=2\times \frac{11^{\frac{3}{4}}}{11}\sqrt[4]{8}\right)\\y=\frac{\sqrt[4]{24750x^{4}-288000}}{15x}\text{; }y=-\frac{\sqrt[4]{24750x^{4}-288000}}{15x}\text{, }&|x|\geq \frac{2\times 22^{\frac{3}{4}}}{11}\end{matrix}\right.$$