Question

find a if 6 upon 3 root 2 minus 2 root 3 is equals to 3 root 2 minus a root 3

Answer 1

Hey friend,
Here is the answer you were looking for:
$\frac{6}{3 \sqrt{2} - 2 \sqrt{3} } = 3 \sqrt{2} - a \sqrt{3} \\ \\ on \: rationalizing \: the \:denominator \: we \: get \\ \\ = \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} } \\ \\ using \: the \: identity \\ (a + b)(a - b) = {a}^{2} - {b}^{2} \\ \\ \frac{6 \times 3 \sqrt{2} + 6 \times 2 \sqrt{3} }{ {(3 \sqrt{2}) }^{2} - {(2 \sqrt{3} )}^{2} } \\ \\ = \frac{18 \sqrt{2} + 12 \sqrt{3} }{18 - 12} \\ \\ = \frac{18 \sqrt{2} + 12 \sqrt{3} }{6} \\ \\ = 3 \sqrt{2} + 2 \sqrt{3} = 3 \sqrt{2} - a \sqrt{3} \\ \\ a = - 2$

Hope this helps!!!

@Mahak24

Thanks...
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