Question
Answer
$$(\dfrac{1+\sqrt{5}}{2})^2=\dfrac{3+\sqrt{5}}{2}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(\frac{1+\sqrt{5}}{2})^2& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{1+\sqrt{5}+\sqrt{5}+5}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6+2\sqrt{5}}{4} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{3+\sqrt{5}}{2}\end{aligned} $$ | |
| ① | $$ (\frac{1+\sqrt{5}}{2})^2 = \left( \frac{1 + \sqrt{5}}{2} \right) \cdot \left( \frac{1 + \sqrt{5}}{2} \right) = \frac{1 + \sqrt{5} + \sqrt{5} + 5}{4} $$ |
| ② | Simplify numerator and denominator |
| ③ | Divide both numerator and denominator by 2. |
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