Question

if x = (2-√3) then (x² + 1/x²) = ?​

Answer 1

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Answer 2

$\sf \: QUESTION: \: if x = (2-√3) then (x² + \frac{1}{x} ²) = ?$

ANSWER-:

$x = 2 - \sqrt{3}$

So,

$\frac{1}{x } = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} }$

$= \frac{2 + \sqrt{3} }{(2) {}^{2} - (\sqrt{3) {}^{2} } }$

$= \frac{2 + \sqrt{3} }{4 - 3}$

$= \frac{2 + \sqrt[]{3} }{1}$

$= 2 + \sqrt{3}$

Now,

$(x {}^{2} + \frac{1}{x} {}^{2} ) = (x + \frac{1}{x} ) {}^{2} - 2$

$= (2 - \sqrt{ \cancel3} + 2 + \sqrt{ \cancel3} ) {}^{2} - 2$

$= (4) {}^{2} - 2$

$= 16 - 2$

$= 14$

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