Question

find the values of a and b if



please answer guys i need a great help!!!​

Answer 1

$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3} \\ \\ \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = a + b \sqrt{3} \\ \\ \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24 }{49 - 48} = a + b \sqrt{3} \\ \\ 11 - 6 \sqrt{3} = a + b \sqrt{3} \\ comparing \: both \: sides \\ a = 11 \\ b = - 6$