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Alexxandr [17]
3 years ago
11

Express

Mathematics
1 answer:
Ann [662]3 years ago
8 0
◆ NUMBER SYSTEMS ◆

\frac{7 - 3 \sqrt{3} }{2 +  \sqrt{3} }  \\  \\ rationalising \: the \: denominator \: , \\  \\  \frac{7 - 3 \sqrt{3} }{2 +  \sqrt{3} }  \times  \frac{2 -  \sqrt{3} }{2 -  \sqrt{3} }  \\  \\  =  \frac{(7 - 3 \sqrt{3})(2 -  \sqrt{3})  }{ {2}^{2} -  { \sqrt{3} }^{2}  }  \\  \\  =  \frac{14 - 7 \sqrt{3} - 6 \sqrt{3}  + 9 }{4 - 3}  \\  \\  =  \frac{23 - 13 \sqrt{3} }{1}  \\  \\  = 23 - 13 \sqrt{3}  = a + b \sqrt{3}  \\  \\ comparing \: both \: sides \: , \\   we \: get \: , \\  \\ a = 23 \\ and \:   , \: \\ b =  - 13
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