Question

Two numbers are in ratio 2:3. The difference
of their cubes is 9,728. Find the numbers.​

Answer 1

Answer:

(3X)^2 - (2X)^2 = 320

9X^2 - 4X^2 = 320

5X^2 = 320

X^2 = 64

X = 8

3X = 24 ; 24 / 8 = 3

2X = 16 ; 16 / 8 = 2

24^2 = 576

16^2 = 256

576 - 256 = 320

The numbers are 16 and 24.

Answer 2

Step-by-step explanation:

let two numbers are in the ratio of 2x:3x

From the question,

${(3x)}^{3} - {(2x)}^{3} = 9728$

$27 {x}^{3} - 8 {x}^{3} = 9728$

$19 {x}^{3} = 9728$

${x}^{3} = 9728 \div 19$

${x}^{3} = 512$

$x = \sqrt[3]{512}$

$x = 8$

Therefore the numbers are

2x and 3x that is

2*8 and 3*8

ans = 16 and 24