Question

$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + ...} } } }$
solve it









plz​

Answer 1

Answer:

$\text{let}\text{ \: x= \:} \sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + \ldots \ldots \ldots} } } }$

Step-by-step explanation:

$\color{navy}\begin{array}{ll}= & \tt x=\sqrt{6+x} & \text { (On squaring both sides) } \\ \\ = & \tt x^{2}=(\sqrt{6+x})^{2} & \\ \\ = & \tt x^{2}=6+x & \\ \\ = & \tt x^{2}-x-6=0 & \\ \\ = & \tt x^{2}-3 x+2 x-6=0 & \\ \\ = & \tt x(x-3)+2(x-3)=0 & \\ \\ = & \tt (x-3)(x+2)=0 & \\ \\ = & \tt (x-3)=0 \quad \text { Or } \quad(x+2)=0 \\ \\ = & \tt x=3 \qquad\text { Or } \qquad \tt x=-2 \\ \\ \text { Thus } & \tt x=3,-2 & \end{array}$