Question

2 + 3 √3 divided by 7 - 2 √3 = a + b √3 . find a and b​

Answer 1

Answer:

The answer of 2+3√3/7-2√3 is 2-11√3/7

Answer 2

Step-by-step explanation:

$\frac{2 + \sqrt{3} }{7 - 2 \sqrt{3} } = a + b \sqrt{3} \\ \\ = \frac{(2 + \sqrt{3}) }{(7 - 2 \sqrt{3}) } \times \frac{(7 + 2 \sqrt{3}) }{(7 + 2 \sqrt{3} )} \\ \\ = \frac{2(7 + 2 \sqrt{3}) + \sqrt{3}(7 + 2 \sqrt{3} ) }{ {7}^{2} - {(2 \sqrt{3}) }^{2} } \\ \\ = \frac{14 + 4 \sqrt{3} + 7 \sqrt{3} + 6 }{49 - 12} \\ \\ = \frac{20 + 11 \sqrt{3} }{37} = a + b \sqrt{3} \\ \\ hence \\a = \frac{20}{37} \\ \\ b = \frac{11}{37}$