Question

If both a and b are rational numbers, find the values of a and b when (4+√5/ 4 - √5) +
(4 - √5/ 4+√5) = a + b√5

Answer 1

Answer:

a=42/11 b=0

Step-by-step explanation:

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

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

$\frac{16 + 5 + 8 \sqrt{5} + 16 + 5 - 8 \sqrt{5} }{16 - 5} = a + b \sqrt{5}$

$\frac{42}{11} = a + b \sqrt{5}$

$a = \frac{42}{11} \: b = 0$

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