Question

gys please help me in the question and give me explanation
if $if \sqrt[3]{\frac{x}{729} } + \sqrt[3]{\frac{8x}{729} } + \sqrt[3]{\frac{27x}{5832} } =1$
then find the value of x

Answer 1

$\frac{ \sqrt[3]{x} }{9} + \frac{2 \sqrt[3]{x} }{9} + \frac{3 \sqrt[3]{x} }{18} = 1 \\ let \: \sqrt[3]{x} = t \\ 2t + 4 t + 3t = 18 \\ 9t = 18 \\ t = \frac{18}{9} = t = 2 \\ \sqrt[3]{x} = 2 \\ x = 8$