Question

Please solve this question.​

Answer 1

Answer:

$\frac{1 + \sqrt{29} }{2}$

Step-by-step explanation:

$\sqrt{7 + \sqrt{7 + \sqrt{7....} } } = x \\ \\ \sqrt{7 + x} = x \\ \\ 7 + x = {x}^{2} \\ \\ {x}^{2} - x - 7 = 0 \\ \\ x = \frac{1 \pm \sqrt{1 + 4 \times 7} }{2} = \frac{1 \pm \sqrt{29} }{2}$

Note that x > 0 , so ignore negative value .