Question

For what value of a and b, (2-√5)/(2+√5)=a+b√5​

Answer 1

$\frac{2 - \sqrt{5} }{2 + \sqrt{5} } = a + b \sqrt{5} \\ \\ \frac{2 - \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} } = a + b \sqrt{5} \\ \\ \frac{4 + 5 - 4 \sqrt{5} }{4 - 5} = a + b \sqrt{5} \\ \\ - 9 + 4 \sqrt{5} = a + b \sqrt{5} \\ \\ comparing \: both \: sides \\ a = - 9 \: \: \: \: \: \: \: \: \: \: \: b = 4$

Answer 2

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