Question

If x - 1/x = √3, then the value of x² + 1/ x² is

1 point

a. 2

b. 9

c. 5

d. None of the above​

Answer 1

Answer:

$x - \frac{1}{x } = \sqrt{3} \\ squaring \: both \: the \: side \\ {(x - \frac{1}{x}) }^{2} = { (\sqrt{3} )}^{2} \: \: \: \: \: \: \: \: ( {(a - b)}^{2} = {a}^{2} + {b}^{2} + 2ab) \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 \times x \times \frac{1}{x} = 3 \\ {x}^{2} + \frac{1}{ {x}^{2} } - 2 = 3 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 3 + 2 \\ {x}^{2} + \frac{1}{ {x}^{2} } = 5$

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