Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784.

1.	Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the numbers.
Answer» Let the ratio 1:2:3 as x, 2x and 3x According to the question, ^x3 + (2x)³ + (3x)³ = 98784 x³ + 8x³ + 27x³ = 98784 36x³ = 98784 x³ = 98784/36 = 2744 x = ∛2744 = ∛(2×2×2×7×7×7) = 2×7 = 14 So, the numbers are, x = 14 2x = 2 × 14 = 28 3x = 3 × 14 = 42

Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the numbers.

Answer»

Let the ratio 1:2:3 as x, 2x and 3x

According to the question,

^x3 + (2x)³ + (3x)³ = 98784

x³ + 8x³ + 27x³ = 98784

36x³ = 98784

x³ = 98784/36

= 2744

x = ∛2744 = ∛(2×2×2×7×7×7)

= 2×7 = 14

So, the numbers are,

x = 14

2x = 2 × 14

= 28

3x = 3 × 14

= 42