Question

Find the value of a and b 5+2root 3 divided by 7+ 4 root 3 = a+ b root 3

Answer 1

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Your answer
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$\frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a \: + b \sqrt{3} \\ \\ now \\ - - - - \\ \\ we \: will \: rationalise \: the \: denominator \\ \\ \frac{(5 + 2 \sqrt{3} )}{(7 + 4 \sqrt{3} )} \times \frac{(7 - 4 \sqrt{3} )}{(7 - 4 \sqrt{3}) } \\ \\ = > \frac{(5 + 2 \sqrt{3} )(7 - 4 \sqrt{3}) }{(7) {}^{2} - (4 \sqrt{3} ) {}^{2} } \\ \\ = > \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{49 - 48} \\ \\ = > \frac{11 - 6 \sqrt{3} }{1 } \\ \\ = > 11 - 6 \sqrt{3} = a \: + b \sqrt{3} \\ \\ so \\ - - - - \\ \\ a \: = 11 \: and \: b = - 6$
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