The correct option is A 2 Let x = √(2+√(2+ √(2+ ... ∞))) ⇒ x^2 = 2 + √(2+√(2+ √(2+ ... ∞))) ⇒ x^2 = 2 + x ⇒ x^2 x 2 = 0 ⇒(x 2) (x+1) = 0 ⇒ x = 1,2 1 i ...

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Byju's Answer

Standard X

Mathematics

Solving Using Quadratic Formula When D>0

The value of ...

Question

The value of $\sqrt{2 + \sqrt{2 + \sqrt{2 + . . . . . . . . .}}}$ is

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Solution

The correct option is A
2

Let $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + . . . \infty}}} \Rightarrow x^{2} = 2 + \sqrt{2 + \sqrt{2 + \sqrt{2 + . . . \infty}}} \Rightarrow x^{2} = 2 + x \Rightarrow x^{2} - x - 2 = 0 \Rightarrow (x - 2) (x + 1) = 0 \Rightarrow x = - 1, 2$
- 1 is neglected
$∴ x = 2 \Rightarrow \sqrt{2 + \sqrt{2 +} \sqrt{2} + . . .} = 2$

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The value of √2+√2+√2+... ... ... is

The correct option is A 2 Let x=√2+√2+√2+...∞⇒x2=2+√2+√2+√2+...∞⇒x2=2+x⇒x2−x−2=0⇒(x−2)(x+1)=0⇒x=−1,2 - 1 is neglected ∴x=2⇒√2+√2+√2+...=2

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