Question 1

Simplify: $$\sqrt{6 + \sqrt{6 + \sqrt{6 + \sqrt{6 + .......}}}}$$

Solution

Let say , $$x=\sqrt{6+\sqrt{6+\sqrt{6............\ }\ }}.$$

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

or,$$x^2-x-6=0.$$

or,$$x^2-3x+2x-6=0.$$

or,$$x\left(x-3\right)+2\left(x-3\right)=0.$$

or,$$\left(x+2\right)\left(x-3\right)=0.$$

So, either x=3 or x=-2.

But negative value is possible.

A is correct choice.

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