x^4-625=0
You asked:
Solve the equation \({x}^{4} - 625 = 0\) for the variable \(x\).
MathBot Answer:
The solutions are given by the formula: \[x = 5 \cos{\left(\frac{\pi k}{2} \right)} + 5 \sin{\left(\frac{\pi k}{2} \right)} i\] 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: \[\begin{aligned}x &= 5\\x &= -5\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}x &= 5 i\\x &= -5 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).