Question

if X=5-√3/5+√3 and y=5+√3/5-√3 show that x²-y²= -10√3/11

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Answer 1

Step-by-step explanation:

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Answer 2

$x = \frac{5 - \sqrt{3} }{5 + \sqrt{3} } \\ \\ x = \frac{5 - \sqrt{3} }{5 + \sqrt{3} } \times \frac{5 - \sqrt{3} }{5 - \sqrt{3} } \\ \\ x = \frac{ {(5 - \sqrt{3}) }^{2} }{ {5}^{2} - { \sqrt{3} }^{2}} \\ \\ x = \frac{25 - 10 \sqrt{3} + 3 }{25 - 3} \\ \\ x = \frac{28 - 10 \sqrt{3} }{22} \\ \\ x = \frac{14 - 5 \sqrt{3} }{11}.$

$y = \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \\ \\ y = \frac{5 + \sqrt{3} }{5 - \sqrt{3} } \times \frac{5 + \sqrt{3} }{5 + \sqrt{3} } \\ \\ y = \frac{ {5 + \sqrt{3} }^{2} }{ {5}^{2} - { \sqrt{3} }^{2} } \\ \\ y = \frac{25 + 10 \sqrt{3} + 3 }{25 - 3} \\ \\ y = \frac{28 + 10 \sqrt{3} }{22} \\ \\ y = \frac{14 + 5 \sqrt{3} }{11}$

$x - y = \frac{14 - 5 \sqrt{3} }{11} - \frac{14 + 5 \sqrt{3} }{11} \\ \\ x - y = \frac{14 - 5 \sqrt{3} - 14 - 5 \sqrt{3} }{11} \\ \\ x - y = \frac{ - 10 \sqrt{3} }{11}$