(C) Given $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$Squaring both sides,we get $x^2 = 2 + \sqrt{2 + \sqrt{2 + \dots}}$Since the expression inside th

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(C) Given $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$Squaring both sides,we get $x^2 = 2 + \sqrt{2 + \sqrt{2 + \dots}}$Since the expression inside the square root is $x$,we can write $x^2 = 2 + x$Rearranging the terms,we get $x^2 - x - 2 = 0$Factoring the quadratic equation: $(x - 2)(x + 1) = 0$This gives $x = 2$ or $x = -1$Since the square root of a positive number must be positive,$x$ cannot be $-1$.Therefore,$x = 2$.

Class 11 Mathematics 4-2.Quadratic Equations and Inequations Solution of quadratic equations and Nature of roots

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The value of $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$ is

A
$-1$
B
$1$
C
$2$
D
$3$

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4-2.Quadratic Equations and Inequations

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Solution of quadratic equations and Nature of roots

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The value of $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$ is

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