0= 1- 8/(t + 1)^3
You asked:
Solve the equation \(0 = 1 - \frac{8}{{\left( t + 1 \right)}^{3}}\) for the variable \(t\).
MathBot Answer:
The solutions are given by the formula: \[t = \left(-1 + 2 \cos{\left(\frac{2 \pi k}{3} \right)}\right) + 2 \sin{\left(\frac{2 \pi k}{3} \right)} i\] 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: \[\begin{aligned}t &= 1\end{aligned}\]
Solutions with nonzero imaginary part: \[\begin{aligned}t &= -2 + \sqrt{3} i \\&= -2 + 1.7320508 i\\t &= -2 - \sqrt{3} i \\&= -2 -1.7320508 i\end{aligned}\]
\(i\) is the imaginary unit, defined as \(i^2 = -1\).