Question

rationalize the factor of 2 + root 3 upon 2 minus root 3 + 2 minus root 3 upon 2 + root 3​

Answer 1

Answer:

14

Step-by-step explanation:

$\frac{2 + \sqrt{3} }{2 - \sqrt{3} } + \frac{2 - \sqrt{3} }{2 + \sqrt{3} } \\ \\ = \frac{(2 + \sqrt{3} )^{2} }{(2 - \sqrt{3})(2 + \sqrt{3} ) } + \frac{ {(2 - \sqrt{3}) }^{2} }{(2 + \sqrt{3})(2 - \sqrt{3} ) } \\ \\ = \frac{ {2}^{2} + { (\sqrt{3}) }^{2} + 2 \times 2 \sqrt{3} }{ {2}^{2} - {( \sqrt{3} )}^{2} } + \frac{ {2}^{2} + {( \sqrt{3}) }^{2} - 2 \times 2 \sqrt{3} }{ {2}^{2} - { (\sqrt{3}) }^{2} } \\ \\ = \frac{4 + 3 + 4 \sqrt{3} }{4 - 3} + \frac{4 + 3 - 4 \sqrt{3} }{4 - 3} \\ \\ = 7 + 4 \sqrt{3} + 7 - 4 \sqrt{3} \\ = 14$

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