3x^4 = 3888
You asked:
Solve the equation \(3 \cdot {x}^{4} = 3888\) for the variable \(x\).
MathBot Answer:
The solutions are given by the formula: \[x = 6 \cos{\left(\frac{\pi k}{2} \right)} + 6 \sin{\left(\frac{\pi k}{2} \right)} i\] where \(k\) is an integer in \(0 \le k < 4\).
There are \(2\) real solutions.
There are \(2\) solutions with nonzero imaginary part.
Real solutions: \[\begin{aligned}x &= 6\\x &= -6\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}x &= 6 i\\x &= -6 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).