Question

Please answer the one in the attachment

14 th question..?

Answer 1

$let \: \: x = \sqrt{a + \sqrt{a + \sqrt{a + ..........} } } \: \: \: \\ \: \: \ = > x = \sqrt{a + x} \: \\ squaring \: on \: both \: sides \: we \: get \\ \: \: \: \: = > {x}^{2} \ = a + x \\ \: \: \: \: = > {x}^{2} - x - a = 0 \\ \: \: \: solving \: this \: quadratic \: \\ equation \: we \: get \\ \: \: \: \: \: x = (1 + \sqrt{1 + 4a}) \div 2 \: or \: (1 - \sqrt{1 + 4a} ) \div 2.$
But x= (1-√(4a+1))/2 will not be my solution because x non-negative quantity
and a should also be non negative for real solution.

I hope you will get it.