Question

Three natural numbers are in ratio 1: 2: 3 . If the sum of their cubes is 972, find the numbers

Answer 1

let the Three natural numbers are in ratio 1: 2: 3 is 1x 2x 3x
x cube + (3x) cube + (2x) cube=972
x^3 + 27x^3+8 x^3 = 972
36x3=972
x^3=972÷36
x^3=27
x=3

then the numbers is 1x=3×1=3
2x=2×3=6
3x=3×3=9
then numbers is 3,6,9
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Answer 2

Ratio  = Number 1 : Number 2 : Number 3 = 1 : 2 : 3

Define x:

Let x be the constant ratio

Number 1 : Number 2 : Number 3 = 1x : 2x : 3x

Define equation:

Given that sun of their cubes is 972

x³ + (2x)³ + (3x)³ - 972

Solve x:

x³ + 8x³ + 27x³ = 972

36x³ = 972

x³ = 27

x = ∛27

x = 3

Find the numbers:

Number 1 : Number 2 : Number 3 = 1x : 2x : 3x

Number 1 = x = 3

Number 2 = 2x = 2(3) = 6

Number 3 = 3x = 3(3) = 9

Answer: The numbers are 3, 6 and 9