Question

find a and b is 5 + 2 root 3 / 7 + 4 root 3 is equal to a + b root 3

Answer 1

First we need to rationalize the given number...
$(5 + 2 \sqrt{3} \div 7 + 4 \sqrt{3}) \times (7 - 4 \sqrt{3} \div 7 - 4 \sqrt{3}$
$= (35 - 20 \sqrt{3} + 14 \sqrt{3} - 8 \times 3) \div ( {7}^{2} - {4 \sqrt{3} }^{2}$
$= (11 - 6 \sqrt{3} ) \div (49 - 48)$
$= 11 - 6 \sqrt{3}$
THIS IS YOUR ans...that a=11 and b=-6