Question

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Please help me ...

$\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x} } } } .... \infty = 4$

Here , $\infty$ = infinity

Find the value of x.

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Thanks for answering !

Answer 1

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HERE'S THE ANSWER...

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Answer 2

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$\mathbb{METHOD\: OF\: SOLUTION:-}$



$\mathsf{\huge{Question:-}}$

$\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x} } } } .... \infty = 4$

Here,

√x it's shows Consecutive Factorization.

so it's must be used Squaring method before it must take constant value of this Equation be 'x'

According the Question;

Squaring on both Sides(LHS and RHS):-

${x+(\sqrt{x + \sqrt{x + \sqrt{x + \sqrt{x} } } } .... \infty }^{2} ) = x = {4}^{2} \\ \\ \\ {x}^{2} = x \: \: \: \: Or\: 16$

Consecutive Number of 16 =4×4
Thus,

Smallest Factor is taken Negative and Largest Factor as same as per Smallest '4'

Here, Equation formed ;

16=x+4

16-4=x

12=x

•°• x=12

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If we taken Negative terms of value must be Answer;

16=x-4

16+4=x

20=x

Hence, x=20

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Here, Positive Consecutive Number must be take ,So
Answer :- 12 for this Question!!

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