Question

Solve it please. step by step.​

Answer 1

Answer:

x = 3

Step-by-step explanation:

Let $x$ = $\sqrt{6+\sqrt{6+\sqrt{6+.......} } }$  --------------(1)

    $x^{2}$ = 6+$\sqrt{6+\sqrt{6+........} }$

   $x^{2} = 6 + x$

   $x^{2} -x -6 =0$

   ($x$-3)($x$+2) =0

Therefore, x = 3, -2.

But -2 is not possible.So, x = 3.

Answer 2

Answer:

x=3

Step-by-step explanation:

x^{2}x

2

= 6+\sqrt{6+\sqrt{6+........} }

6+

6+........

x^{2} = 6 + xx

2

=6+x

x^{2} -x -6 =0x

2

−x−6=0

(xx -3)(xx +2) =0

Therefore, x = 3, -2.