Question

If x=2 + root 3 find value of x^2 +1/x^2

Answer 1

Answer:

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☯️Here's ur answer...☆☆☆

Step-by-step explanation:

$\huge{ \mid{ \pink{ \overline{ \underline{ \orange{answer....}}}}}}$

$\large{x = 2 + \sqrt{3} } \\ = \large{ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } } \\ = \large{ \frac{2 - \sqrt{3} }{(2 + \sqrt{3})(2 - \sqrt{3}) } } \\ = \large{ \frac{2 - \sqrt{3} }{2 {}^{2} - ( \sqrt{3}) {}^{2} } } \\ \large{ by \: using(a + b)(a - b) = {a}^{2} - {b}^{2}} \\ \\ = 2 - \sqrt{3} \\ \large{ \red{ = to \: find... {x}^{2} + \frac{1}{x {}^{2} } }} \\ = > \large{x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} } \\ \large{ = > x + \frac{1}{x} = 4} \\ = > \large{(x + \frac{1}{x} ) {}^{2} = 16} \\ = > \large{ {x}^{2} + \frac{1}{ {x}^{2} } + 2 = 16} \\ = > \large{ \green{ {x}^{2} + \frac{1}{ {x}^{2} } = 14}} (\blue{answer})$

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