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Three numbers are In the ratio $2: 3: 4$. The sum of their cubes is $33957$. Find the numbers.
Given: Three numbers are In the ratio $2: 3: 4$. The sum of their cubes is $33957$.
To do: To find the numbers.
Solution:
Let the numbers be $2x,\ 3x$ and $4x$.
sum of cubes$=33957$
$\Rightarrow (2x)^3 + (3x)^3 + (4x)^3=33957$
$\Rightarrow 8x^3 + 27x^3 + 64x^3=33957$
$\Rightarrow 99x^3=33957$
$\Rightarrow x^3=\frac{33957}{99}=343$
$\Rightarrow x=\sqrt[3]{343}=7$
Numbers are:
$2x=2\times7=14$
$3x=3\times7=21$
$4x=4\times7=28$
Thus, the numbers are: $14,\ 21,\ 28$.
Updated on: 10-Oct-2022
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