Question

please show working of this sum in proper form
correct ans is a=(-61/29) & b=(-24/29)

i have an exam tomorrow so its urgent
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Answer 1

$\frac{1 + \sqrt{48} }{5 \sqrt{3} + 4 \sqrt{2} - \sqrt{72} - \sqrt{108} + \sqrt{8} + 2 } = a + b \sqrt{3} \\ \\ \frac{1 + 4\sqrt{3} }{5 \sqrt{3} + 4 \sqrt{2} - 6 \sqrt{2} -6 \sqrt{3} +2 \sqrt{2} + 2 } = a + b \sqrt{3} \\ \\ \frac{1 + 4\sqrt{3} }{2 - \sqrt{3} } = a + b \sqrt{3} \\ \\ \frac{1 + 4\sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } = a + b \sqrt{3} \\ \\ \frac{2 + \sqrt{3} + 4\sqrt{3} (2 + \sqrt{3} )}{4 - 3 } = a + b \sqrt{3} \\ \\2 + \sqrt{3} + 8 \sqrt{3} + 12 = a + b \sqrt{3}\\ \\ {14 + 9 \sqrt{3} } = a + b \sqrt{3} \\ \\ \boxed{\begin{array}{c} \bf \: a = 14 \\ \bf \: b = 9 \end{array}}$