((1 + sqrt(3))/2)^3 + ((1 - sqrt(3))/2)^3

asked by guest
on Nov 17, 2024 at 12:51 am



You asked:

Evaluate the expression: \({\left( \frac{1 + \sqrt{3}}{2} \right)}^{3} + {\left( \frac{1 - \sqrt{3}}{2} \right)}^{3}\)

MathBot Answer:

\[{\left( \frac{1 + \sqrt{3}}{2} \right)}^{3} + {\left( \frac{1 - \sqrt{3}}{2} \right)}^{3} = \left(\frac{1}{2} - \frac{\sqrt{3}}{2}\right)^{3} + \left(\frac{1}{2} + \frac{\sqrt{3}}{2}\right)^{3} \approx 2.5\]

\[\begin{aligned}{\left( \frac{1 + \sqrt{3}}{2} \right)}^{3} + {\left( \frac{1 - \sqrt{3}}{2} \right)}^{3}& = \left(\left(1 + \sqrt{3}\right) \cdot \frac{1}{2}\right)^{3} + \left(\left(1 - \sqrt{3}\right) \cdot \frac{1}{2}\right)^{3}\\& = \left(\frac{1}{2} + \frac{1}{2} \cdot \sqrt{3}\right)^{3} + \left(\left(1 - \sqrt{3}\right) \cdot \frac{1}{2}\right)^{3}\\& = \left(\frac{1}{2} + \frac{1}{2} \cdot \sqrt{3}\right)^{3} + \left(\frac{1}{2} - \frac{1}{2} \cdot \sqrt{3}\right)^{3}\end{aligned}\]

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