11/108=22/(x-3)^3
You asked:
Solve the equation \(\frac{11}{108} = \frac{22}{{\left( x - 3 \right)}^{3}}\) for the variable \(x\).
MathBot Answer:
The solutions are given by the formula: \[x = \left(3 + 6 \cos{\left(\frac{2 \pi k}{3} \right)}\right) + 6 \sin{\left(\frac{2 \pi k}{3} \right)} i\] where \(k\) is an integer in \(0 \le k < 3\).
There is \(1\) real solution.There are \(2\) solutions with nonzero imaginary part.
Real solutions: \[\begin{aligned}x &= 9\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}x &= 3 \sqrt{3} i \\&\approx 5.1961524 i\\x &= - 3 \sqrt{3} i \\&\approx -5.1961524 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).