Question

Find the A and B ....

Answer 1

5+2√3/(7+4√3) rationalize it
(5+2√3)(7-4√3)/(49-48)
=35-20√3+14√3-24
=11-7√3
so comparing with right hand side
a=11
b=-7

Answer 2

$\frac{5 + 2 \sqrt{3} }{7 + 4\sqrt{3} } = a + b\sqrt{3}$
$\frac{5 + 2\sqrt{3} }{7 + 4\sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = a + b3$
$\frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{49 - 48} = a + b \sqrt{3}$
$11 - 6 \sqrt{3 } = a + b \sqrt{3}$

Therefore,
a=11 & b=-6


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