Question

find a and b if 5+3√3/7+4√3=a+b√3​

Answer 1

$</p><p>\sf \rightarrow \quad \dfrac{5 + 3 \sqrt{3} }{7 + 4 \sqrt{3} } = a + b \sqrt{3} \\ \\ \sf \rightarrow \quad \frac{5 + 3 \sqrt{3} }{7 + 4 \sqrt{3} } \times \frac{7 - 4 \sqrt{3} }{7 - 4 \sqrt{3} } = a + b \sqrt{3} \\ \\ \sf \rightarrow \quad \frac{(5 + 3 \sqrt{3} )(7 - 4 \sqrt{3}) }{ {7}^{2} - {(4 \sqrt{3} )}^{2} } = a + b \sqrt{3} \\ \\ \sf \rightarrow \quad \frac{35 - 20 \sqrt{3} + 21 \sqrt{3} + 3 \sqrt{3} \cdot - 4 \sqrt{3} }{49 - 48} = a + b \sqrt{3} \\ \\ \sf \rightarrow \quad - 1 + \sqrt{3} = a + b \sqrt{3} \\ \\ \sf \quad On \: comparing, \\ \\ \sf \qquad a = - 1 \qquad b = 1</p><p>$