Solve y^frac{1{6}}=x^frac{1{8}}+26+sqrt{(291)^sqrt{2/2}}

$$y ^ { \frac { 1 } { 6 } } = x ^ { \frac { 1 } { 8 } } + 26 + \sqrt { ( 291 ) ^ { \frac { \sqrt { 2 } } { 2 } } }$$

Solve for x (complex solution)

$$\left\{\begin{matrix}x=\left(-\sqrt[6]{y}+291^{\frac{\sqrt{2}}{4}}+26\right)^{8}\text{, }&arg(-\left(-\sqrt[6]{y}+291^{\frac{\sqrt{2}}{4}}+26\right))<\frac{\pi }{4}\\x=0\text{, }&y=156\times 291^{\frac{5\sqrt{2}}{4}}+10140\times 291^{\sqrt{2}}+351520\times 291^{\frac{3\sqrt{2}}{4}}+6854640\times 291^{\frac{\sqrt{2}}{2}}[phone]\times 291^{\frac{\sqrt{2}}{4}}+291^{\frac{3\sqrt{2}}{2}}[phone]\end{matrix}\right.$$

Solve for y (complex solution)

$$y=\left(\sqrt[8]{x}+291^{\frac{\sqrt{2}}{4}}+26\right)^{6}$$

$$arg(\sqrt[8]{x}+291^{\frac{\sqrt{2}}{4}}+26)<\frac{\pi }{3}$$

Solve for x

$$x=\left(-\sqrt[6]{y}+291^{\frac{\sqrt{2}}{4}}+26\right)^{8}$$

$$y\geq 0\text{ and }-\left(-\sqrt[6]{y}+291^{\frac{\sqrt{2}}{4}}+26\right)\geq 0$$

Solve for y

$$y=\left(\sqrt[8]{x}+291^{\frac{\sqrt{2}}{4}}+26\right)^{6}$$

$$x\geq 0$$