Question

find rational number a and b such that root 2 -5 by 2+root5=a root 5+b

Answer 1

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