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