Question
Answer
$$(4-3\sqrt{7})(\sqrt{7}+1)=\sqrt{7}-17$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}(4-3\sqrt{7})(\sqrt{7}+1)& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}4\sqrt{7}+4-21-3\sqrt{7} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\sqrt{7}-17\end{aligned} $$ | |
| ① | $$ \color{blue}{ \left( 4- 3 \sqrt{7}\right) } \cdot \left( \sqrt{7} + 1\right) = \color{blue}{4} \cdot \sqrt{7}+\color{blue}{4} \cdot1\color{blue}{- 3 \sqrt{7}} \cdot \sqrt{7}\color{blue}{- 3 \sqrt{7}} \cdot1 = \\ = 4 \sqrt{7} + 4-21- 3 \sqrt{7} $$ |
| ② | Combine like terms |
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