Question
Answer
$$\dfrac{3}{5+\sqrt{17}}=\dfrac{15-3\sqrt{17}}{8}$$
Explanation
Tap the blue circles to see an explanation.
| $$ \begin{aligned}\frac{3}{5+\sqrt{17}}& \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle1}{\textcircled {1}} } }}}\frac{3}{5+\sqrt{17}}\frac{5-\sqrt{17}}{5-\sqrt{17}} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle2}{\textcircled {2}} } }}}\frac{15-3\sqrt{17}}{25-5\sqrt{17}+5\sqrt{17}-17} \xlongequal{ } \\[1 em] & \xlongequal{ \color{blue}{ \text{\normalsize{ \htmlClass{explanationCircle explanationCircle3}{\textcircled {3}} } }}}\frac{15-3\sqrt{17}}{8}\end{aligned} $$ | |
| ① | Multiply the numerator and denominator by the conjugate of the denominator . $$\color{blue}{ 5- \sqrt{17}} $$. |
| ② | Multiply in a numerator. $$ \color{blue}{ 3 } \cdot \left( 5- \sqrt{17}\right) = \color{blue}{3} \cdot5+\color{blue}{3} \cdot- \sqrt{17} = \\ = 15- 3 \sqrt{17} $$ Simplify denominator. $$ \color{blue}{ \left( 5 + \sqrt{17}\right) } \cdot \left( 5- \sqrt{17}\right) = \color{blue}{5} \cdot5+\color{blue}{5} \cdot- \sqrt{17}+\color{blue}{ \sqrt{17}} \cdot5+\color{blue}{ \sqrt{17}} \cdot- \sqrt{17} = \\ = 25- 5 \sqrt{17} + 5 \sqrt{17}-17 $$ |
| ③ | Simplify numerator and denominator |
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