Question

7-3root5 / 2-root5= a+b root 5
find a and b​

Answer 1

$\frac{7 - 3 \sqrt{5} }{2 - \sqrt{5} } = a + b \sqrt{5} \\ \\ \frac{7 - 3 \sqrt{5} }{2 - \sqrt{5} } \times \frac{2 + \sqrt{5} }{2 + \sqrt{5} } = a + b \sqrt{5} \\ \\ \frac{14 + 7 \sqrt{5} - 6 \sqrt{5} - 15}{4 - 5} = a + b \sqrt{5} \\ \\ \frac{ - 1 + \sqrt{5} }{ - 1} = a + b \sqrt{5} \\ \\ 1 - \sqrt{5} = a + b \sqrt{5} \\ \\ comparing \: both \: sides \\ a = 1 \\ b = - 1$