Question

Three numbers are in the ratio 1:2:3. The sum of their cubes is 98784. Find the Numbers. PLEASE HELP ME TO SOLVE THIS QUESTION

Answer 1

let the no. be x, 2x and 3x

ATQ

x³ + (2x)³ + (3x)³ = 98784
x³ + 8x³ + 27x³ = 98784

9x³ + 27x³ = 98784

36x³       = 98784

x³            = 98784 / 36
x³             = 2744
x              = ∛2× 2×2×7×7×7
x               = 7× 2
x              = 14 

so the no. are x = 14
                       2x = 28
                       3x = 42

Answer 2

Let the common multiple be x
So their ratio = x,2x,3x
According to given COndition
x³ + (2x)³ + (3x)³ = 98784
x³ + 8x³ + 27x³ = 98784
36x³ = 98784
x³ = 98784/36
x³ = 2744
x = ∛2744
x = 14

So the Numbers are 14,28,42
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