(A) Let $y = \sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$$\Rightarrow y = \sqrt{42+y}$On squaring both sides,we get:$y^2 = 42 + y$$\Rightarrow y^2 - y - 42 =

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(A) Let $y = \sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$$\Rightarrow y = \sqrt{42+y}$On squaring both sides,we get:$y^2 = 42 + y$$\Rightarrow y^2 - y - 42 = 0$Factorizing the quadratic equation:$(y - 7)(y + 6) = 0$$\Rightarrow y = 7$ or $y = -6$Since the square root function must yield a non-negative value,$y = -6$ is rejected.Therefore,the required solution is $y = 7$.

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

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The value of $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

AP EAMCET 2004 All AP EAMCET

TS EAMCET 2004 All TS EAMCET

A
$7$
B
$-6$
C
$5$
D
$4$

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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 $\sqrt{42+\sqrt{42+\sqrt{42+\ldots}}}$ is equal to:

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