Question

If x = 3 + V3 , then what is the value is x² + 9/x² ?​

Answer 1

Answer:

9 is the answer

put the values you will get the answer

Answer 2

Answer

$\frac{30 + 9 \sqrt{3} }{2}$

Step By Step Solution

${x}^{2} + \frac{9}{ {x}^{2} } = { \left(x + \frac{3}{x} \right)}^{2} - 6 \\ = { \left((3 + \sqrt{3}) + \frac{3(3 - \sqrt{3}) }{(3 + \sqrt{3})(3 - \sqrt{3})}\right)}^{2} - 6 \\ = { \left((3 + \sqrt{3}) + \frac{(3 - \sqrt{3}) }{2} \right)}^{2} - 6 \\ = { \left( \frac{6 + 2 \sqrt{3} + 3 - \sqrt{3} }{2} \right)}^{2} - 6 \\ = { \left( \frac{9 + \sqrt{3} }{2} \right)}^{2} - 6 \\ = \frac{81 + 3 + 18 \sqrt{3} }{4} - 6 \\ = \frac{84 - 24 + 18 \sqrt{3} }{4} \\ = \frac{60 + 18 \sqrt{3} }{4} = \frac{30 + 9 \sqrt{3} }{2}$