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 ...

You visited us 3 times! Enjoying our articles? Unlock Full Access!

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

Right on! Give the BNAT exam to get a 100% scholarship for BYJUS courses

No worries! We‘ve got your back. Try BYJU‘S free classes today!

Open in App

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
$∴ x = 2 \Rightarrow \sqrt{2 + \sqrt{2 +} \sqrt{2} + . . .} = 2$

Suggest Corrections

Similar questions

Q. The value of

(\sqrt{2} + \sqrt{2}) (\sqrt{2} - \sqrt{2})

is _____.

Q. Find the value of

\frac{\sqrt{2 + \sqrt{2 + \sqrt{2 + \sqrt{2}}}}}{2}

Q. The value of

l o g_{\sqrt{\sqrt{2}}} \cdot \sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2}}}}}

is .....

The value of $\sqrt{2 \sqrt{2} \sqrt{2 \dots \dots \dots \infty}}$ is 2.

Q. The value of

\sqrt{2 \sqrt{2 \sqrt{2 \sqrt{2}}}}

Join BYJU'S Learning Program

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

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