Question

Find the values of a and b in each of the following
√5-1/√5 + 1+√5+1/√5-1 = a + b√5​

Answer 1

Answer:

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Answer 2

Step-by-step explanation:

$\frac{ \sqrt{5} - 1 }{ \sqrt{5} } = \frac{5 - \sqrt{5} }{5}$

(multiplying by root 5)

$1 = \frac{5}{5}$

$\frac{ \sqrt{5} + 1}{ \sqrt{5} - 1 } = \frac{6 + 2 \sqrt{5} }{4}$

(multiplying by root 5 +1 & simplifying)

$\frac{ \sqrt{5} - 1 }{5} + 1 = \frac{5 - \sqrt{5} + 5}{5} = \frac{10 - \sqrt{5} }{5}$

$\frac{10 - \sqrt{5} }{5} + \frac{6 + 2 \sqrt{5} }{4} = \frac{40 - 4 \sqrt{5} + 30 + 10 \sqrt{5} }{20} = \frac{70 + 6 \sqrt{5} }{20} = 3.5 + 0.3 \sqrt{5}$

$a = 3.5 \: b = 0.3$