Question

X=2-√3 Find 1/X and X3+1/x3​

Answer 1

Answer:

$\frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } = \frac{2 + \sqrt{3} }{4 - 3} = 2 + \sqrt{3} \\ then \: \frac{1}{x} = 2 + \sqrt{3} \\ then \: x + \frac{1}{x} = 2 - \sqrt{3} + 2 + \sqrt{3} = {2}^{2} - \sqrt{ {3}^{2} } = 4 - 3 = 1 \\ then \: x + \frac{1}{x} = 1 \\ then \: {x}^{3} + \frac{ 1}{ {x}^{3} } \\ atq \\( 2 - { \sqrt{3} })^{3} +( \frac{1}{2 - {3}^{3} } ) = {1}^{3}$

x + 1/x cube is 1

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