Question

$\sqrt[3]{9 \sqrt[3]{9 \sqrt[3]{9 \sqrt[3]{9....... \infty } } } }$
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Answer 1

Step-by-step explanation:

$y = \sqrt[3]{9 \sqrt[3]{9 \sqrt[3]{9 \sqrt[3]{9......... \infty } } } }$

$y = \sqrt[3]{9y}$

${y}^{3} = 9y$

${y}^{3} - 9y = 0$

$= > y( {y}^{2} - 9) = 0$

$= > y(y - 3)(y + 3) = 0$

since root is a positive quantity so y≠-3

so,

$either \: \: y = 0 \: \: or \: \: y = 3$

Answer 2

$\huge \sf {\orange {\underline {\pink{\underline {♡A᭄ɴsᴡᴇʀ࿐ \ :- }}}}}$