Question

X=2-√3 find x^2+1\x^2

Answer 1

Answer:

$\huge \bf{answer} \\ \implies14 \\ \\ \huge \red{ \bf{explanation}} \\ \\ find \: \implies \: {x}^{2} + \frac{1}{ {x}^{2} } \\ \\ \\ firstly \: find \: {x}^{2} \\ \\ {x}^{2} \implies \: {(2 - \sqrt{3} )}^{2} \\ \\ {x}^{2} \implies \: 4 + 3 - 4 \sqrt{3} \\ \\ {x}^{2} \implies \: 7 - 4 \sqrt{3} \\ \\ now \: find \: \frac{1}{ {x}^{2} } \\ \\ \frac{1}{ {x}^{2} } \implies \: \frac{1}{7 - 4 \sqrt{3} } \\ by \: rationalising \\ \\ \frac{1}{ {x}^{2} } \implies \: \frac{7 + 4 \sqrt{3} }{49 - 48} \\ \\ \frac{1}{ {x}^{2} } \implies \: 7 + 4 \sqrt{3} \\ \\ now \: \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 7 - 4 \sqrt{3} + 7 + 4 \sqrt{3} \\ \\ \red{ \boxed{{x}^{2} + \frac{1}{ {x}^{2} } = 14}} \\ \\ \\ hope \: it \: helps \: you$