Question

If x =2 + √3 find x2 + 1/x 2 =? ​

Answer 1

Answer:

${x}^{2} + \frac{1}{ {x}^{2} } = 14.$

Step-by-step explanation:

$x = 2 + \sqrt{3} \\ \\ \\ \\ \frac{1}{x} = \frac{1}{2 + \sqrt{3} } = \frac{1}{2 + \sqrt{3} } \times \frac{2 - \sqrt{3} }{2 - \sqrt{3} } = 2 - \sqrt{3} \\ \\ x + \frac{1}{x} = 2 + \sqrt{3} + 2 - \sqrt{3} = 4 \\ \\ \\ \\ \\ {(x + \frac{1}{x} )}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ {4}^{2} = {x}^{2} + \frac{1}{ {x}^{2} } + 2 \\ \\ therefore \: \: {x}^{2} + \frac{1}{ {x}^{2} } = 16 - 2 \\ \\ {x}^{2} + \frac{1}{ {x}^{2} } = 14.$

Answer 2

Answer:

The answer to this question is 14.