The value of x = sqrt{2 + sqrt{2 + sqrt{2 + d | vedclass

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(C) Given the expression $x = \sqrt{2 + \sqrt{2 + \sqrt{2 + \dots}}}$.Since the expression repeats infinitely,we can write $x = \sqrt{2 + x}$.Squaring

Vedclass · Accepted Answer

$2$

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

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

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