Question

Find the value ofa and b, if 6-4√3 / 6+4√3 = a+b√3

Answer 1

Answer:

$\frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } = \frac{6 - 4 \sqrt{3} }{6 + 4 \sqrt{3} } \times \frac{6 - 4 \sqrt{3} }{6 - 4 \sqrt{3} } =$

$\frac{36 - 2 \times 6 \times 4 \sqrt{3} + 48 }{36 - 48} = \frac{84 - 48 \sqrt{3} }{ - 12} = - 7 + 4 \sqrt{3}$

$i.e \: \: - 7 + 4 \sqrt{3} = a + b \sqrt{3}$

so a = –7 & b = 4.

Ans.