Question

if(4+root5)/(4-root5)=(a+broot5),find the value of a and b​

Answer 1

Step-by-step explanation:

$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } \times \frac{4 + \sqrt{5} }{4 + \sqrt{5} } = a + b \sqrt{5} \\ \frac{( {4 + \sqrt{5)} }^{2} }{ {4}^{2} - { \sqrt{5} }^{2} } \\ = \frac{ {4}^{2} + \sqrt{5}^{2} + 2 \times 4 \times \sqrt{5} }{16 - 5} \\ = \frac{16 + 5 + 8 \sqrt{5} }{11} = \frac{21 + 8 \sqrt{5} }{11} \\ so \: \: \frac{21 + 8 \sqrt{5} }{11} = a + b \sqrt{5} \\ hence \: \: a = \frac{21}{11} \: and \: b = \frac{8}{11}$