Question

If √5-2/√5+2 =a+b√5, find a and b

Answer 1

Step-by-step explanation:

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Answer 2

Step-by-step explanation:

$\frac{ \sqrt{5} - 2}{ \sqrt{5} + 2 } = a + b \sqrt{5} \\ = > \frac{ \sqrt{5} - 2 }{ \sqrt{5} + 2 } \times \frac{ \sqrt{5} - 2 }{ \sqrt{5} - 2} = a + b \sqrt{5} \\ = > \frac{ {( \sqrt{5} - 2)}^{2} }{ ( \sqrt{5} ) - {(2)}^{2} } = a + b \sqrt{5} \\ = > \frac{ { \sqrt{5} }^{2} + {2}^{2} - 2 \times \sqrt{5} \times 2 }{5 - 4} = a + b \sqrt{5} \\ = > \frac{5 + 4 - 4 \sqrt{5} }{1} = a + b \sqrt{5} \\ = > 9 - 4 \sqrt{5} = a + b \sqrt{5} \\ \\ on \: comparing \: we \: get \\ \\ a = 9 \\ b = - 4$