If frac 2 sqrt 3 - sqrt 2 sqrt 3 2 sqrt 2 m n 6... - JAMB Mathematics 2017 Question

(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}})= m + n√6

(\frac{2 \sqrt{3} - \sqrt{2}}{\sqrt{3} + 2 \sqrt{2}}) x (\frac{\sqrt{3} - 2 \sqrt{2}}{\sqrt{3} - \sqrt{2}})

(\frac{2 \sqrt{3} (\sqrt{3} - 2 \sqrt{2}) - \sqrt{2}(\sqrt{3} - 2 \sqrt{2})}{\sqrt{3}(\sqrt{3} - 2 \sqrt{2}) + 2 \sqrt{2}(\sqrt{3} - 2 \sqrt{2})})

(\frac{2 \times 3 - 4\sqrt{6} - 6 + 2 \times 2}{3 - 2 \sqrt{6} + 2 \sqrt{6} - 4 \times 2})

= (\frac{6 - 4 \sqrt{6} - \sqrt{6} + 4}{3 - 8})

= (\frac{0 - 4 \sqrt{6} - 6}{5})

= (\frac{10 - 5 \sqrt{6}}{5})

= − 2 + √6

∴ m + n(\sqrt{6}) = − 2 + √6

m = − 2, n = 1