Question

If a = 2- √3 / 2, then find the value of a²+1 / a²​

Answer 1

Answer:

$5 + 2 \sqrt{3}$

Step-by-step explanation:

$a = \frac{2 - \sqrt{3} }{2} \\ \frac{ {a}^{2} + 1}{ {a}^{2} } = \frac{ {a}^{2} }{ {a}^{2} } + \frac{1}{ {a}^{2} } \\ = 1 + \frac{1}{ {a}^{2} } \\ = 1 + \frac{1}{ \frac{2 - \sqrt{3} }{2} } \\ = 1 + \frac{2}{2 - \sqrt{3} } \\ = \frac{(2 - \sqrt{3}) + 2}{2 - \sqrt{3} } \\ = \frac{4 - \sqrt{3} }{2 - \sqrt{3} } \\ rationalising \\ = \frac{4 - \sqrt{3} }{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ = \frac{4(2 + \sqrt{3}) - \sqrt{3} (2 \ + \sqrt{3}) }{ {(2)}^{2} - (\sqrt{3} )^{2} } \\ = \frac{8 + 4 \sqrt{3} - 2 \sqrt{3} - 3 }{4 - 3} \\ = 5 + 2 \sqrt{3}$

Answer 2

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