Question 120

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

Solution

we need to find value of $$\sqrt{6+\sqrt{6+\sqrt{6+...}}}$$

let $$\sqrt{6+\sqrt{6+\sqrt{6+...}}}$$ = x

here x = $$\sqrt{6+x}$$

on squaring both sides

$$x^2 - x - 6$$ = 0

x = 3 , x = -2

here -2 will be rejected as square root can not give negative value and hence x = 3

$$\sqrt{6+\sqrt{6+\sqrt{6+...}}}$$ = 3

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