Question

find a if 6/3root2 - 2root 3 = 3 root 2 - aroot 3​

Answer 1

$\frac{6}{3 \sqrt{2} } - 2 \sqrt{3} = 3 \sqrt{2} - x \sqrt{3} \\ = > \sqrt{2} - 2 \sqrt{3 } = 3 \sqrt{2} - x \sqrt{3} \\ = > x = \frac{2 \sqrt{2} + 2 \sqrt{3} }{ \sqrt{3} }$

Answer 2

$\frac{6}{3√2 - 2√3} = (3√2 - a√3)$

$from \: rationalising \: in \: L.H.S$

$\frac{6(3√2 + 2√3)}{(3√2 - 2√3)(3√2 + 2√3)}= (3√2 - a√3)$

$\frac{6(3√2 + 2√3)}{(3√2)² - (2√3)²} = (3√2 - a√3)$

$\frac{6(3√2 + 2√3)}{18 - 12} = (3√2 - a√3)$

$\frac{6(3√2 + 2√3)}{6} = (3√2 - a√3)$

$(3√2 + 2√3) = (3√2 - a√3)$

$From \: Comparing \: both \: side -$

$a = -2$