(C) Given $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$.Since the expression is infinite,we can write $x = \sqrt{6 + x}$.Squaring both sides,we

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(C) Given $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$.Since the expression is infinite,we can write $x = \sqrt{6 + x}$.Squaring both sides,we get $x^2 = 6 + x$,where $x > 0$.Rearranging the terms,we get $x^2 - x - 6 = 0$.Factoring the quadratic equation: $(x - 3)(x + 2) = 0$.Since $x > 0$,we must have $x = 3$.

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

Medium

If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$,then which of the following is true?

A
$x$ is an irrational number.
B
$2 < x < 3$
C
$x = 3$
D
None of these.

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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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MediumAP EAMCET 2025

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If $x = \sqrt{6 + \sqrt{6 + \sqrt{6 + \dots \infty}}}$,then which of the following is true?

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If $\alpha$ is a root of multiplicity $3$ of the equation $x^5-8x^4+25x^3-38x^2+28x-8=0$,then $\alpha^2-5\alpha+6=$

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