Question

$\sqrt{20 + \sqrt{20 + \sqrt{20 + \sqrt{20... \infty } } } }$
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Answer 1

Answer:

$\huge\underbrace\mathtt\pink{Hypothetical Question}$

Answer 2

To FinD :

$\rightsquigarrow \sf \sqrt{20 + \sqrt{20 + \sqrt{20 + \dots \infty } } } = { }^{}$

SolutioN :

$\: \: \: \circ\sf \: \: \: \: \: \sqrt{20 + \sqrt{20 + \sqrt{20 + \dots \infty } } } = x \: \: \: \: \: \: \: \:[ let ]$

$\implies\sf 20 + \sqrt{20 + \sqrt{20 + \dots \infty } } = {x}^{2}$

$\implies\sf 20 + x = {x}^{2} \: \: \: \: \: \: \: \: \: \: \: \: \: \: \: [ \sf \because \: \sqrt{20 + \sqrt{20 + \sqrt{20 + \dots \infty } } } = x ]$

$\implies \sf \: {x}^{2} - x - 20 = 0$

$\implies \sf \: (x - 5)(x + 4) = 0$

$\implies \sf \: { { \sf{x = 5 \: \: \: \: \: or \: \: \: \: \: x = - 4}}}$

$\: \: \: \circ \: \: \: \sf \sqrt{20 + \sqrt{20 + \sqrt{20 + \dots \infty } } } \: \: will \: \: never \: - ve \: \:$

$\therefore \underline{ \boxed{ \sf \sqrt{20 + \sqrt{20 + \sqrt{20 + \dots \infty } } } = 5}}$

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