Question

Q (+50)
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Sederhakan
[tex] \sf \frac{8}{4 + 2 \sqrt{3} } = ...[/tex]
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Answer 1

[tex]\frac{8}{4 + 2 \sqrt{3} } \\ [/tex][tex] = \frac{ \not8}{ \not2(2 + \sqrt{3} )} \\ [/tex][tex] = \frac{4}{2 + \sqrt{3} } \\ [/tex][tex] = \frac{4}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } \\ [/tex][tex] = \frac{4(2 - \sqrt{3} )}{(2 + \sqrt{3} )(2 - \sqrt{3} )} \\ [/tex][tex] = \frac{4(2 - \sqrt{3}) }{ {2}^{2} - \sqrt{ {3}^{2} } } \\ [/tex][tex] = \frac{4(2 - \sqrt{3}) }{(2 \times 2) - 3} \\ [/tex][tex] = \frac{4(2 - \sqrt{3}) }{4 - 3} \\ [/tex][tex] = \frac{4(2 - \sqrt{3} )}{1} \\ [/tex][tex] = 4(2 - \sqrt{3} ) \\ [/tex][tex] = \bold{ 8 - 4 \sqrt{3} } \\ [/tex]