Question

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

Answer:

3.28

Step-by-step explanation:

$\frac{ \sqrt{5} }{2 + \sqrt{5} } - \frac{5}{2} + 4 \\ = (\frac{ \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} }) - \frac{5}{2} + \frac{4}{1} \\ = \frac{2 \sqrt{5} - 5 }{4 - 5} - \frac{5}{4} + 4 \\ = \frac{20 - 8 \sqrt{5} - 5 + 16 }{4} \\ = \frac{31 - 8\sqrt{5} }{4} \\ = \frac{31 - 8 \times 2.23}{4} \\ = \frac{13.15}{4} \\ = 3.28$

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Answer 2

$\frac{ \sqrt{5} }{2 + \sqrt{5} } - \frac{5}{2} + 4 \\ = (\frac{ \sqrt{5} }{2 + \sqrt{5} } \times \frac{2 - \sqrt{5} }{2 - \sqrt{5} }) - \frac{5}{2} + \frac{4}{1} \\ = \frac{2 \sqrt{5} - 5 }{4 - 5} - \frac{5}{4} + 4 \\ = \frac{20 - 8 \sqrt{5} - 5 + 16 }{4} \\ = \frac{31 - 8\sqrt{5} }{4} \\ = \frac{31 - 8 \times 2.23}{4} \\ = \frac{13.15}{4} \\ = 3.28$