Three numbers are to one another 2:3:4. The sum of their cubes is 0.33

1.	Three numbers are to one another 2:3:4. The sum of their cubes is 0.334125. Find the numbers.
Answer» Let the ratio 2:3:4 be 2a, 3a, and 4a. So according to the question: (2a)³+ (3a)³+(4a)³ = 0.334125 8a³+27a³+64a³ = 0.334125 99a³ = 0.334125 a³ = 334125/1000000×99 = 3375/1000000 a = ∛(3375/1000000) = ∛((15×15×15)/ 100×100×100) = 15/100 = 0.15 Hence ,the numbers are: 2×0.15 = 0.30 3×0.15 = 0.45 = 4×0.15 = 0.6

Three numbers are to one another 2:3:4. The sum of their cubes is 0.334125. Find the numbers.

Answer»

Let the ratio 2:3:4 be 2a, 3a, and 4a.

So according to the question:

(2a)³+ (3a)³+(4a)³ = 0.334125

8a³+27a³+64a³ = 0.334125

99a³ = 0.334125

a³ = 334125/1000000×99

= 3375/1000000

a = ∛(3375/1000000)

= ∛((15×15×15)/ 100×100×100)

= 15/100

= 0.15

Hence ,the numbers are:

2×0.15 = 0.30

3×0.15 = 0.45

= 4×0.15

= 0.6