Answer:
[tex]\huge\boxed{2\sqrt[3]{\dfrac{33457}{99}};\ 3\sqrt[3]{\dfrac{33457}{99}};\ 4\sqrt[3]{\dfrac{33457}{99}}}[/tex]
Step-by-step explanation:
[tex]\text{Let}\ x-\text{some number}.\\\\\text{Theree numbers are in the ratio}\ 2:3:4\to 2x:3x:4x.\\\\2x,\ 3x,\ 4x-\text{the numbers you are looking for}\\\\33,457-\text{the sum of their cubes}\\\\\bold{The\ equation:}\\\\(2x)^3+(3x)^3+(4x)^3=33457\\\\\bold{Solution:}\\\\8x^3+27x^3+64x^3=33457\\\\99x^3=33457\qquad|\text{divide both sides by 99}\\\\\dfrac{99x^3}{99}=\dfrac{33457}{99}\\\\x^3=\dfrac{33457}{99}\to x=\sqrt[3]{\dfrac{33457}{99}}[/tex]
[tex]2x=2\sqrt[3]{\dfrac{33457}{99}}\\\\3x=3\sqrt[3]{\dfrac{33457}{99}}\\\\4x=4\sqrt[3]{\dfrac{33457}{99}}[/tex]
