Question 145

The value of expression $$\sqrt{6+\sqrt{6+\sqrt{6+.....\ }}}\ is$$

Solution

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

$$\sqrt{6+(\sqrt{6+\sqrt{6+.....\ }})}=x$$.........(2)

Substitute equation (1) in (2)

$$\sqrt{6+(x)}\ =\ x$$ (or) $$x^{2} - x - 6 = 0$$

$$x = 3, -2$$. But '$$x$$' value should be positive

$$\therefore x = 3$$

Hence, option D is the correct answer.

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