Question

Three numbers are to one another 2 : 3 : 4. The sum of their cubes is 0.334125. Find the numbers.

 

Answer 1

Let the numbers be 2x, 3x and 4x.
According to the question:​

\[\left( 2x \right)^3 + \left( 3x \right)^3 + \left( 4x \right)^3 = 0 . 334125\]

\[ \Rightarrow 8 x^3 + 27 x^3 + 64 x^3 = 0 . 334125\]

\[ \Rightarrow 8 x^3 + 27 x^3 + 64 x^3 = 0 . 334125\]

\[ \Rightarrow 99 x^3 = 0 . 334125\]

\[ \Rightarrow x^3 = \frac{{334125}^{3375}}{1000000 \times 99}\]

\[ \Rightarrow x = \sqrt[3]{\frac{3375}{1000000}}\]

\[ \Rightarrow x = \frac{\sqrt[3]{3375}}{\sqrt[3]{1000000}}\]

\[ \Rightarrow x = \frac{15}{100} = 0 . 15 .\]

Thus, the numbers are:

\[2 \times 0 . 15 = 0 . 30 \]

\[3 \times 0 . 15 = 0 . 45\]

\[4 \times 0 . 15 = 0 . 60\]