Question

Find rational numbers a and b
2-√5/2+√5=a√5+b

Answer 1

$2 - \frac{ \sqrt{5} }{2} + \sqrt{5} = a \sqrt{5} + b \\ \frac{4 - \sqrt{5} + 2 \sqrt{5} }{2} = a \sqrt{5} + b \\ \frac{4}{2} + \frac{ \sqrt{5} }{2} = a \sqrt{5} + b \\ \frac{1}{2} \sqrt{5} + 2 = a \sqrt{5} + b \\ comparing \: both \: side \: we \: get \\ a = \frac{1}{2} \: and \: b \: = 2.$