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

asked by guest
on Nov 17, 2024 at 12:52 am



You asked:

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

MathBot Answer:

\[{\left( \frac{1 + \sqrt{3}}{2} \right)}^{2} + {\left( \frac{1 - \sqrt{3}}{2} \right)}^{2} = \left(\frac{1}{2} - \frac{\sqrt{3}}{2}\right)^{2} + \left(\frac{1}{2} + \frac{\sqrt{3}}{2}\right)^{2} \approx 2.0\]

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

+ Submit Question