Question

plzz answer with explanation ​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

We have,

$\frac{4 + \sqrt{5} }{4 - \sqrt{5} } = a + b \sqrt{5}$

$\implies \frac{(4 + \sqrt{5} )(4 + \sqrt{5} )}{(4 - \sqrt{5} )(4 + \sqrt{5}) } = a + b \sqrt{5}$

$\implies \frac{ {(4)}^{2} + 2 \times 4 \times \sqrt{5} + ( \sqrt{5}) ^{2} }{( {4})^{2} -( { \sqrt{5} })^{2} } = a + b \sqrt{5}$

$\implies \frac{16 + 4 \sqrt{5} + 5}{16 - 5} = a + b \sqrt{5}$

$\implies \frac{21 + 4 \sqrt{5} }{11} = a + b \sqrt{5}$

$\implies (\frac{21}{11} ) + ( \frac{4}{11} ) \sqrt{5} = a + b \sqrt{5}$

So,

a = (21/11) and b = (4/11)