2465=(1/2x)^1/2*(3/2x)^3/2

asked by guest
on Oct 25, 2024 at 6:24 am



You asked:

Solve the equation \(2465 = \frac{\frac{{\left( \frac{1}{2 x} \right)}^{1}}{2} \cdot {\left( \frac{3}{2 x} \right)}^{3}}{2}\) for the variable \(x\).

MathBot Answer:

The solutions are given by the formula: \[x = \frac{\sqrt{2} \cdot 7395^{\frac{3}{4}} \cos{\left(\frac{\pi k}{2} \right)}}{9860} + \frac{\sqrt{2} \cdot 7395^{\frac{3}{4}} \sin{\left(\frac{\pi k}{2} \right)}}{9860} i\] 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: \[\begin{aligned}x &= \frac{\sqrt{2} \cdot 7395^{\frac{3}{4}}}{9860} \\&\approx 0.11437779\\x &= - \frac{\sqrt{2} \cdot 7395^{\frac{3}{4}}}{9860} \\&\approx -0.11437779\end{aligned}\]

Solutions with nonzero imaginary part: \[\begin{aligned}x &= \frac{\sqrt{2} \cdot 7395^{\frac{3}{4}}}{9860} i \\&\approx 0.11437779 i\\x &= - \frac{\sqrt{2} \cdot 7395^{\frac{3}{4}}}{9860} i \\&\approx -0.11437779 i\end{aligned}\]

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

+ Submit Question