Question

three numbers are in the ratio 2:3:4. If the sum of their cubes is 6336, find the numbers

Answer 1

$\bf \large \it{ Hey \: User!!!}$

according to the question, three numbers are in ratio 2 : 3 : 4 and the sum of their cubes is 6336.

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

therefore (2x)³ + (3x)³ + (4x)³ = 6336
>> 8x³ + 27x³ + 64x³ = 6336
>> 99x³ = 6336
>> x³ = 6336/99
>> x³ = 64
>> x = √(4 × 4 × 4)
>> x = 4

hence, the numbers are :-

2x = 2 × 4 = 8, 3x = 3 × 4 = 12 and 4x = 4 × 4 = 16

$\bf \large \it \: Cheers!!! \:$

Answer 2

(2x)^3+(3x)^3+(4x)^3=6336
8x^3+27x^3+64x^3=6336
99x^3=6336
×^3=6336/99
x^3=64
x=4
no are 8,12,16