Question

5+2√3/7+4√3=a-b√3 find the value of a and b
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Answer 1

[tex]\mathfrak{ \huge{Answer:-} } \\\bold{ \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } = a - b \sqrt{3} } \\ \frac{5 + 2 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4\sqrt{3} }{7 - 4 \sqrt{3} } = a - b \sqrt{3} \\ \frac{(5 + 2 \sqrt{3})(7 - 4 \sqrt{3})}{(7 + 4 \sqrt{3})(7 - 4\sqrt{3})} = a - b \sqrt{3} \\ \frac{5(7 - 4 \sqrt{3})+ 2 \sqrt{3}(7 - 4 \sqrt{3})}{ {(7)}^{2} - {(4 \sqrt{3} )}^{2} } = a - b \sqrt{3} \\ \frac{35 - 20 \sqrt{3} + 14 \sqrt{3} - 24}{49 - 48} = a - b \sqrt{3} \\ \frac{11 - 6 \sqrt{3} }{1} = a - b \sqrt{3} \\ 11 - 6 \sqrt{3} = a - b \sqrt{3} \\ \bold{ \large{ \boxed{ \boxed{a = 11, \: b = 6} } } } [/tex]