Question

three numbers are in ratio 2:3:4.the sum of their cubes is 0.334125.find the numbers

Answer 1

let the numbers are 2x,3x,4x

given
${(2x)}^{3} + {( 3x)}^{3} + {(4x)}^ 3 = 0.334125\\ 8x^{3} + 27 {x}^{3} + 64 {x}^{3} = 0.334125 \\ 99 {x}^{3} = 0.334125 \\ {x}^{3} = 0.003375 \\ x = 0.15$
the numbers are 0.3,0.45,0.6

Answer 2

since the numbers are in the ratio 2:3:4 .Then
let 2x,3x,and 4x be the numbers .then
Given condition.,
(2x)^3+(3x)^3+(4x)^3 = 0.334125
8x^3+27x^3+64x^3 = 0.334125
99x^3 = 0.334125
x^3 = 0.003375
x= 0.15

Hence , the three numbers are
2×0.15= 0.3
3×0.15 = 0.45
4×0.15 = 0.6

hope it helps you.