Question

Three number are in the ratio 3:4:5 and sum their cubes 1728. Find the number.​

Answer 1

Step-by-step explanation:

let the 3 numbers be 3x, 4x, 5x

(3x)³+(4x)³+(5x)³= 1728

27x^3 +64x^3 +125x^3 =1728

216x^3   = 1728

x^3= 1728/216

x^3  = 8

x =2

Numbers are: 6,8,10

Answer 2

Let the numbers be 3x, 4x and 5x.

$= > {(3x + 4x + 5x)}^{3} = 1728 \\ \\ = > {3x}^{3} + {4x}^{3} + {5x}^{3} + 6(5x)(4x)(3x) + 3( {3x}^{2} (4x) + {4x}^{2} (5x) + {5x}^{2} (3x) + {4x}^{2} (3x) + (4x) {5x}^{2} + (5x) {3x}^{2} ) = 1728 \\ \\ = > 1728x = 1728 \\ \\ = > x = 1$

So numbers are 3, 4 and 5.