Question
Answer
$$(-3+\sqrt{5})\cdot(-6-\sqrt{5})=13-3\sqrt{5}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(-3+\sqrt{5})\cdot(-6-\sqrt{5})& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}18+3\sqrt{5}-6\sqrt{5}-5 \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}13-3\sqrt{5}\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( -3 + \sqrt{5}\right) } \cdot \left( -6- \sqrt{5}\right) = \color{blue}{-3} \cdot-6\color{blue}{-3} \cdot- \sqrt{5}+\color{blue}{ \sqrt{5}} \cdot-6+\color{blue}{ \sqrt{5}} \cdot- \sqrt{5} = \\ = 18 + 3 \sqrt{5}- 6 \sqrt{5}-5 $$ |
| ② | Combine like terms |
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