Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.3341

1.	Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.
Answer» Let us assume the three number be 2a, 3a, 4a Then, Given, sum of cube of three numbers is 0.334125 i.e. (2a)³ + (3a)³ + (4a)³ = 0.334125 8a³ + 27a³ + 64a³ = 0.334125 99a³ = 0.334125 a³ = 0.334125/99 a³ = 0.003375 a³ = 3375/1000000 a = ³√(3375/1000000) a = ³√((15 × 15 × 15)/(10 × 10 × 10 × 10 × 10 × 10)) a = ³√(15³/10⁶) a = 15/1000 a = 0.015 ∴The numbers are, 2a = 2 × 0.015 = 0.03 3a = 3 × 0.015 = 0.045 4a = 4 × 0.015 = 0.06

Three numbers are in the ratio 2:3:4. The sum of their cubes is 0.334125. Find the numbers.

Answer»

Let us assume the three number be 2a, 3a, 4a

Then,

Given, sum of cube of three numbers is 0.334125

i.e. (2a)³ + (3a)³ + (4a)³ = 0.334125

8a³ + 27a³ + 64a³ = 0.334125

99a³ = 0.334125

a³ = 0.334125/99

a³ = 0.003375

a³ = 3375/1000000

a = ³√(3375/1000000)

a = ³√((15 × 15 × 15)/(10 × 10 × 10 × 10 × 10 × 10))

a = ³√(15³/10⁶)

a = 15/1000

a = 0.015

∴The numbers are, 2a = 2 × 0.015 = 0.03

3a = 3 × 0.015 = 0.045

4a = 4 × 0.015 = 0.06