![\huge\boxed{2\sqrt[3]{\dfrac{33457}{99}};\ 3\sqrt[3]{\dfrac{33457}{99}};\ 4\sqrt[3]{\dfrac{33457}{99}}}](/tpl/images/0858/8314/66784.png)
![\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}}](/tpl/images/0858/8314/d4b6c.png)
![2x=2\sqrt[3]{\dfrac{33457}{99}}\\\\3x=3\sqrt[3]{\dfrac{33457}{99}}\\\\4x=4\sqrt[3]{\dfrac{33457}{99}}](/tpl/images/0858/8314/49a31.png)
Three numbers are in the ratio 2:3:4. The sum of their cubes is 33, 457,
Find the numbers:...
Mathematics, 01.11.2020 14:00 sarabell5326
Three numbers are in the ratio 2:3:4. The sum of their cubes is 33, 457,
Find the numbers:
Answers: 3
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