Question

Find a and b if 7+√3 / 7-√3=a+b√3 *
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Answer 1

$\frac{7 + \sqrt{3} }{7 - \sqrt{3} } = a + b \sqrt{3} \\ \frac{7 + \sqrt{3} }{7 - \sqrt{3} } \times \frac{7 + \sqrt{3} }{7 + \sqrt{3} } = a + b \sqrt{3} \\ \frac{49 + 3 + 14 \sqrt{3} }{49 - 3} = a + b \sqrt{3} \\ \frac{52 + 14 \sqrt{3} }{46} = a + b \sqrt{3} \\ \frac{26 + 7 \sqrt{3} }{23} = a + b \sqrt{3} \\ \frac{26}{23} + \frac{7}{23} \sqrt{3} = a + b \sqrt{3} \\ comparing \: both \: sides \\ a = \frac{26}{23} \\ b = \frac{7}{23}$