If $ \frac{2\sqrt{3}-\sqrt{2}}{\sqrt{3}+2\sqrt{2}} = m + n\sqrt{6} $, find the values of m and n respectively.

Assessment: JAMB UTME - Mathematics - 2017 Subject: General Mathematics

Question 1 Report

1, − 2

− 2, n = 1

\frac{- 2}{5}

, 1

\frac{2}{3}

Answer Details

\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}}

\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

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Surds (radicals)

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If \( \frac{2\sqrt{3}-\sqrt{2}}{\sqrt{3}+2\sqrt{2}} = m + n\sqrt{6} \), find the values of m and n respectively.

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If \( \frac{2\sqrt{3}-\sqrt{2}}{\sqrt{3}+2\sqrt{2}} = m + n\sqrt{6} \), find the values of m and n respectively.

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