2+2+2+......−−−−−−−√−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−√is equal to ?2+2+2+......is equal to ?\eqalign{ & \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & {\text{is equal to ?}} \cr} " /> 2+2+2+......−−−−−−−√−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−√is equal to ?2+2+2+......is equal to ?\eqalign{ & \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & {\text{is equal to ?}} \cr} " /> 2+2+2+......−−−−−−−√−−−−−−−−−−−−√−−−−−−−−−−−−−−−−−√is equal to ?2+2+2+......is equal to ?\eqalign{ & \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & {\text{is equal to ?}} \cr} " />

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$\begin{aligned} \sqrt{2 + \sqrt{2 + \sqrt{2 + . . . . . .}}} \\ is equal to ? \end{aligned}$ $\eqalign{ & \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & {\text{is equal to ?}} \cr}$

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Answer:- 1

Explanation:-

Solution:

\begin{aligned} x = \sqrt{2 + \sqrt{2 + \sqrt{2 + . . . . . .}}} \\ \Rightarrow x^{2} = 2 + \sqrt{2 + \sqrt{2 + . . . . . . .}} \\ \Rightarrow x^{2} = 2 + x \\ \Rightarrow x^{2} - x - 2 = 0 \\ \Rightarrow x (x - 2) + 1 (x - 2) = 0 \\ \Rightarrow (x + 1) (x - 2) = 0 \\ \Rightarrow x = 2 \end{aligned}

$\eqalign{ & x = \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & \Rightarrow {x^2} = 2 + \sqrt {2 + \sqrt {2 + .......} } \cr & \Rightarrow {x^2} = 2 + x \cr & \Rightarrow {x^2} - x - 2 = 0 \cr & \Rightarrow x\left( {x - 2} \right) + 1\left( {x - 2} \right) = 0 \cr & \Rightarrow \left( {x + 1} \right)\left( {x - 2} \right) = 0 \cr & \Rightarrow x = 2 \cr}$

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", "text": "

\begin{aligned} \sqrt{2 + \sqrt{2 + \sqrt{2 + . . . . . .}}} \\ is equal to ? \end{aligned}

$\eqalign{ & \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & {\text{is equal to ?}} \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" }, "answerCount": "4", "acceptedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x = \sqrt{2 + \sqrt{2 + \sqrt{2 + . . . . . .}}} \\ \Rightarrow x^{2} = 2 + \sqrt{2 + \sqrt{2 + . . . . . . .}} \\ \Rightarrow x^{2} = 2 + x \\ \Rightarrow x^{2} - x - 2 = 0 \\ \Rightarrow x (x - 2) + 1 (x - 2) = 0 \\ \Rightarrow (x + 1) (x - 2) = 0 \\ \Rightarrow x = 2 \end{aligned}

$\eqalign{ & x = \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & \Rightarrow {x^2} = 2 + \sqrt {2 + \sqrt {2 + .......} } \cr & \Rightarrow {x^2} = 2 + x \cr & \Rightarrow {x^2} - x - 2 = 0 \cr & \Rightarrow x\left( {x - 2} \right) + 1\left( {x - 2} \right) = 0 \cr & \Rightarrow \left( {x + 1} \right)\left( {x - 2} \right) = 0 \cr & \Rightarrow x = 2 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM", "author": { "@type": "Person", "name": "Nitin Sir" } }, "suggestedAnswer": { "@type": "Answer", "text": "

Solution:

\begin{aligned} x = \sqrt{2 + \sqrt{2 + \sqrt{2 + . . . . . .}}} \\ \Rightarrow x^{2} = 2 + \sqrt{2 + \sqrt{2 + . . . . . . .}} \\ \Rightarrow x^{2} = 2 + x \\ \Rightarrow x^{2} - x - 2 = 0 \\ \Rightarrow x (x - 2) + 1 (x - 2) = 0 \\ \Rightarrow (x + 1) (x - 2) = 0 \\ \Rightarrow x = 2 \end{aligned}

$\eqalign{ & x = \sqrt {2 + \sqrt {2 + \sqrt {2 + ......} } } \cr & \Rightarrow {x^2} = 2 + \sqrt {2 + \sqrt {2 + .......} } \cr & \Rightarrow {x^2} = 2 + x \cr & \Rightarrow {x^2} - x - 2 = 0 \cr & \Rightarrow x\left( {x - 2} \right) + 1\left( {x - 2} \right) = 0 \cr & \Rightarrow \left( {x + 1} \right)\left( {x - 2} \right) = 0 \cr & \Rightarrow x = 2 \cr}$ ", "dateCreated": "7/24/2019 10:09:12 AM" } }

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