Question

find a and b if 5+root 2/ 5-root 2 =a+b root 2​

Answer 1

Answer:

$\frac{5 + \sqrt{2} }{5 - \sqrt{2} } = a + b \sqrt{2} \\ \frac{5 + \sqrt{2} }{5 - \sqrt{2} } \times \frac{5 + \sqrt{2} }{5 + \sqrt{2} } \: = a + b \sqrt{2} \\ \frac{ {(5 + \sqrt{2}) }^{2} }{ {5}^{2}- {( \sqrt{2}) }^{2} } \: = a + b \sqrt{2} \\ \: \frac{25 + 2 + 10 \sqrt{2} }{25 - 2} = a + b \sqrt{2} \\ \: \frac{27 + 10 \sqrt{2} }{23} = a + b \sqrt{2} \\ \frac{27}{23} + \frac{10 \sqrt{2} }{23} = a + b \sqrt{2} \: \\ a \: = \frac{27}{23} \\ b = \frac{10}{23}$