Question

please answer with full solution​

Answer 1

Answer:

7

Step-by-step explanation:

$x = \frac{2}{3 + \sqrt{7} } \\ x - 3 = \frac{2}{3 + \sqrt{7} } - 3 \\ {(x - 3)}^{2} = { (\frac{2}{3 + \sqrt{7} } - 3)}^{2} \\ = { (\frac{2}{3 + \sqrt{7} } )}^{2} + {3}^{2} - 2 \times \frac{2}{3 + \sqrt{7} } \times 3 \: as \: {(a - b)}^{2} = {a}^{2} + {b}^{2} - 2ab \\ = \frac{4}{ {(3 + \sqrt{7} )}^{2} } + 9 - \frac{12}{3 + \sqrt{7} } \\ = \frac{4}{9 + 7 + 6 \sqrt{7} } + 9 - \frac{12}{3 + \sqrt{7} } \\ = 9 + \frac{4}{16 + 6 \sqrt{7} } - \frac{12}{3 + \sqrt{7} } \\ = 9 + \frac{(12 + 4 \sqrt{7}) - (192 + 72 \sqrt{7} )}{(16 + 6 \sqrt{7}) \times (3 + \sqrt{7} )} \\ = 9 - \frac{180 + 68 \sqrt{7} }{90 + 34 \sqrt{7} } \\ = 9 - 2 \: (as \: \frac{180 + 68 \sqrt{7} }{90 + 34 \sqrt{7} } \: = 2)\\ = 7$