Question

if x square is equal to 2 minus root 3 then find the value of x square + 1
x square​

Answer 1

$x = 2 - \sqrt{3} \\ \\ \frac{1}{x} = \frac{1}{2 - \sqrt{3} } \times \frac{2 + \sqrt{3} }{2 + \sqrt{3} } \\ \\ \: \: \: \: \: = \frac{2 + \sqrt{3} }{4 - 3} = 2 + \sqrt{3}$

Now,

${x}^{2} + \frac{1}{ {x}^{2} } \\ \\ = {(2 - \sqrt{3} )}^{2} + {(2 + \sqrt{3} )}^{2} \\ \\ = (4 + 3 - 4 \sqrt{3} ) + (4 + 3 + 4 \sqrt{3} ) \\ \\ = (7 - 4 \sqrt{3} ) + (7 + 4\sqrt{3} ) \\ \\ = 7 - 4 \sqrt{3} + 7 + 4\sqrt{3} \\ \\ = 14$