Question

Three numbers are in the ratio 2:3:4. The sum of their cubes is 33, 457,
Find the numbers:​

Answer 1

`\huge\boxed{2\sqrt[3]{(33457)/(99)};\ 3\sqrt[3]{(33457)/(99)};\ 4\sqrt[3]{(33457)/(99)}}`

Explanation:

`\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}\\\\(99x^3)/(99)=(33457)/(99)\\\\x^3=(33457)/(99)\to x=\sqrt[3]{(33457)/(99)}`

`2x=2\sqrt[3]{(33457)/(99)}\\\\3x=3\sqrt[3]{(33457)/(99)}\\\\4x=4\sqrt[3]{(33457)/(99)}`