Question
Answer
$$\dfrac{7+3\sqrt{5}}{2}-\dfrac{7-3\sqrt{5}}{2}=3\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{7+3\sqrt{5}}{2}-\frac{7-3\sqrt{5}}{2}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{7+3\sqrt{5}-7+3\sqrt{5}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{6\sqrt{5}}{2} \xlongequal{ } \\[1 em] & \xlongequal{ }3\sqrt{5}\end{aligned} $$ | |
| ① | $$ \frac{7+3\sqrt{5}}{2}-\frac{7-3\sqrt{5}}{2}
= \frac{7+3\sqrt{5}}{2} \cdot \color{blue}{\frac{ 1 }{ 1}} - \frac{7-3\sqrt{5}}{2} \cdot \color{blue}{\frac{ 1 }{ 1}}
= \frac{7+3\sqrt{5}-7+3\sqrt{5}}{2} $$ |
| ② | Simplify numerator and denominator |
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