0.5458*V^4-23.22*10^7=0

asked by guest
on Nov 19, 2024 at 8:20 am



You asked:

Solve the equation \(0.5458 \cdot {V}^{4} - 23.22 \cdot {10}^{7} = 0\) for the variable \(V\).

MathBot Answer:

The solutions are given by the formula: \[V = \frac{100 \cdot 2729^{\frac{3}{4}} \cdot \sqrt[4]{11610} \cos{\left(\frac{\pi k}{2} \right)}}{2729} + \frac{100 \cdot 2729^{\frac{3}{4}} \cdot \sqrt[4]{11610} \sin{\left(\frac{\pi k}{2} \right)}}{2729} i\] 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: \[\begin{aligned}V &= \frac{100 \cdot 2729^{\frac{3}{4}} \cdot \sqrt[4]{11610}}{2729} \\&\approx 143.61744\\V &= - \frac{100 \cdot 2729^{\frac{3}{4}} \cdot \sqrt[4]{11610}}{2729} \\&\approx -143.61744\end{aligned}\]

Solutions with nonzero imaginary part: \[\begin{aligned}V &= \frac{100 \cdot \sqrt[4]{11610} \cdot 2729^{\frac{3}{4}}}{2729} i \\&\approx 143.61744 i\\V &= - \frac{100 \cdot \sqrt[4]{11610} \cdot 2729^{\frac{3}{4}}}{2729} i \\&\approx -143.61744 i\end{aligned}\]

\(i\) is the imaginary unit, defined as \(i^2 = -1\).

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