Let \(A=\sqrt{6+\sqrt{6+\sqrt{6+....}}}>0\)

\(\Rightarrow A^2=6+\sqrt{6+\sqrt{6+...}}\)

\(\Rightarrow A^2=6+A\)\(\Rightarrow A^2-A-6=0\)

\(\Rightarrow\left(A+2\right)\left(A-3\right)=0\)

\(\Rightarrow\left[{}\begin{matrix}A-3=0\\A+2=0\end{matrix}\right.\)\(\Rightarrow A=3\left(A>0\right)\)

Can you make the next question more clearly ?

Let A=√6+√6+√6+....>0A=6+6+6+....>0

⇒A2=6+√6+√6+...⇒A2=6+6+6+...

⇒A2=6+A⇒A2=6+A⇒A2−A−6=0⇒A2−A−6=0

⇒(A+2)(A−3)=0⇒(A+2)(A−3)=0

⇒[A−3=0A+2=0⇒[A−3=0A+2=0⇒A=3(A>0)

Cho A = √ 6 + √ 6 + √ 6 + ....> 0A = 6 + 6 + 6 + ....> 0

⇒A2 = 6 + √ 6 + √ 6 ... ... ⇒A2 = 6 + 6 + 6 + ...

⇒A2 = 6 + A⇒A2 = 6 + A⇒A2-A-6 = 0⇒A2-A-6 = 0

⇒ (A + 2) (A-3) = 0⇒ (A + 2) (A-3) = 0

⇒ [A-3 = 0A + 2 = 0⇒ [A-3 = 0A + 2 = 0⇒A = 3 (A> 0)