Question

Find the value of
$\frac{6}{3 \sqrt{2 } - 2 \sqrt{3} } = 3 \sqrt{2 } - a \sqrt{3}$
​

Answer 1

Answer:

PLEASE SEE THE ATTACHED IMAGE.

a = -2

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Answer 2

Answer:-

LHS:-

$\bf \implies \: \frac{6}{3 \sqrt{2} - 2 \sqrt{3} } \times \frac{3 \sqrt{2} + 2 \sqrt{3} }{3 \sqrt{2} + 2 \sqrt{3} }$

$\bf \implies \: \frac{6(3 \sqrt{2} + 2 \sqrt{3} )}{18 - 12} \\ \\ \bf \implies \: \frac{6(3 \sqrt{2} + 2 \sqrt{3} )}{6} \\ \\ \bf \implies \:3 \sqrt{2} + 2 \sqrt{3} \\ \\ now \\ \\ \bf \implies \: 3 \sqrt{2} - a \sqrt{</u><u>3</u><u>} = 3 \sqrt{2} + 2 \sqrt{3}$

$\bf \implies \: - a \sqrt{3} = 2 \sqrt{3} \\ \\ \bf \implies \: - a = 2 \\ \\ \bf \implies \:a = - 2$