Question

3 no.s are in the ratio 2:3:4. the sum of their cubes is 0.334125 . find the no.s

Answer 1

Let the three numbers be 2x, 3x and 4x.

${(2x)}^{2} + {(3x)}^{2} + {(4x)}^{2} = 0.334125\\ 4 {x}^{2} + 9 {x}^{2} + 16 {x}^{2} = 0.334125\\ 29 {x}^{2} = 0.334125 \\ {x}^{2} = \frac{0.334125}{29} \\ {x}^{2} = 0.01152 \\ x = 0.107 \\ \\ \\ \\ 2x = 2 \times 0.107 = 0.214 \\ \\ 3x = 3 \times 0.107 = 0.321 \\ \\ 4x = 4 \times 0.107 = 0.428$