x^4-(50/(z))=14 equation
The teacher will be very surprised to see your correct solution 😉
The solution
_________
/ 50
x_1 = -I*4 / 14 + --
\/ z
$$x_{1} = - i \sqrt[4]{14 + \frac{50}{z}}$$
_________
/ 50
x_2 = I*4 / 14 + --
\/ z
$$x_{2} = i \sqrt[4]{14 + \frac{50}{z}}$$
_________
/ 50
x_3 = -4 / 14 + --
\/ z
$$x_{3} = - \sqrt[4]{14 + \frac{50}{z}}$$
_________
/ 50
x_4 = 4 / 14 + --
\/ z
$$x_{4} = \sqrt[4]{14 + \frac{50}{z}}$$
Sum and product of roots
[src]
_________ _________ _________ _________
/ 50 / 50 / 50 / 50
-I*4 / 14 + -- + I*4 / 14 + -- + -4 / 14 + -- + 4 / 14 + --
\/ z \/ z \/ z \/ z
$$\left(- i \sqrt[4]{14 + \frac{50}{z}}\right) + \left(i \sqrt[4]{14 + \frac{50}{z}}\right) + \left(- \sqrt[4]{14 + \frac{50}{z}}\right) + \left(\sqrt[4]{14 + \frac{50}{z}}\right)$$
$$0$$
_________ _________ _________ _________
/ 50 / 50 / 50 / 50
-I*4 / 14 + -- * I*4 / 14 + -- * -4 / 14 + -- * 4 / 14 + --
\/ z \/ z \/ z \/ z
$$\left(- i \sqrt[4]{14 + \frac{50}{z}}\right) * \left(i \sqrt[4]{14 + \frac{50}{z}}\right) * \left(- \sqrt[4]{14 + \frac{50}{z}}\right) * \left(\sqrt[4]{14 + \frac{50}{z}}\right)$$
$$-14 - \frac{50}{z}$$