Find the value of - 6- 6 - 6 - 6 - -

The correct option is B 3 √( 6+√( 6+√( 6....∞ #160; ) #160; ) #160; ) Let y=√( 6+√( 6+√( 6....∞ #160; ) #160; ) #160; ) #160; ...

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Byju's Answer

Standard IX

Mathematics

Irrational Numbers on the Number Line

Find the valu...

Question

Find the value of $\sqrt{6 + \sqrt{6} + \sqrt{6} + \sqrt{6} + - - - - - \infty .}$

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Solution

The correct option is B $3$
$\sqrt{6 + \sqrt{6 + \sqrt{6.... \infty}}}$
Let $y = \sqrt{6 + \sqrt{6 + \sqrt{6.... \infty}}}$
$y = \sqrt{6 + y}$
Squaring both sides,
$\Rightarrow y^{2} = 6 + y$
$\Rightarrow y^{2} - y - 6 = 0$
$y^{2} - 3 y + 2 y - 6 = 0$
$y (y - 3) + 2 (y - 3) = 0$
$(y + 2) (y - 3) = 0$
$\Rightarrow y = - 2, 3$
Hence, the answer is $- 2, 3.$
$∵ y \neq - v e$
$∴ y = 3$

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