If x = sqrt{6 + sqrt{6 + sqrt{6 + dots infty} | vedclass

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(C) Given the expression $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$.Since the expression repeats infinitely,we can write it as $x = \sqrt{6 +

Vedclass · Accepted Answer

$x = 3$

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(C) Given the expression $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$.Since the expression repeats infinitely,we can write it as $x = \sqrt{6 + x}$.Squaring both sides,we get $x^2 = 6 + x$,where $x > 0$.Rearranging the terms gives the quadratic equation $x^2 - x - 6 = 0$.Factoring the quadratic equation: $(x - 3)(x + 2) = 0$.This gives $x = 3$ or $x = -2$.Since $x$ must be positive (as it is a square root),we discard $x = -2$.Therefore,$x = 3$.

If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$,then

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