Question

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

Answer 1

Answer:

let the ratio be x

x+2x+3x

x3+8x3+27x3=98784

36x3=98784

x3=98784/36

x3= 2744

x=14 and

2x=28

3x=42

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Answer 2

Answer:

Three numbers are 14, 28, 42.

Step-by-step explanation:

Given that-

The ratio of three numbers = 1 : 2 : 3

Let A, B and C are three numbers. Then-

A = x

B = 2x

C = 3x

According to question-

The sum of the cubes of A, B and C = 98784

$x^{3} +(2x)^{3} + (3x)^{3}  = 98784$

$x^{3} + 8x^{3} + 27x^{3} = 98784$

$36x^{3} = 98784$

$x^{3} = \dfrac{98784}{36}$

$x^{3} = 2744$

$x = \sqrt[3]{2744}$

x = 14

So, A = x

A = 14

B = 2x

  = 2 × 14

B = 28

C = 3x

  = 3 × 14

C = 42

Hence, three numbers are 14, 28, 42.