Question

three number are in a ratio 2:3:4. The sum of their cubes is 72171. Find the numbers. ​

Answer 1

Let the 3 numbers be 2x, 3x, 4x.

Sum of their cubes= 72171

(2x)^3+(3x)^3+(4x)^3=72171

8x+27x+64x=72171

99x=72171

x=72171÷99

x=729

2x= 2×729 = 1458

3x=3×729 = 2187

4x=4×729 = 2916

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Answer 2

The numbers are: 18,27 and 36.

Let the numbers be 2x, 3x, 4x.

Sum of their cubes = 72171

⇒ (2x)³ +(3x)³ +(4x)³ = 72171

⇒  8x³ + 27x³ + 64x³ = 72171

⇒                      99 x³ = 72171

⇒                            x³ =  $\frac{72171}{99}$

⇒                            x³ = 729

⇒                              x =   $\sqrt[3]{729}$  

⇒                              x = 9

∴ The numbers are:

2x = 2 × 9 = 18

3x = 3 × 9 = 27

4x = 4 × 9 = 36

The numbers are: 18,27 and 36.

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