Question

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

Answer 1

Let the numbers be x, 2x and 3x
a/q
x[tex]x^{3} + 8x^{3} + 27x^{3} = 98784 [/tex]
or 
$36 x^{3} = 98784$
or 
$x^{3} = 98784/36$
or 
$x^{3} = 2744$
or
$x = \sqrt[3]{2744}$
or
x = 14

2x= 28
3x= 42

Answer 2

the numbers be y 2y 3y
because their ratio is 1;2;3
given that sum of their cubes is 98784
therefore (Y)^3 +(2y)^3 +(3y)^3= 98784
(y)^3+8(y)^3+27(y)^3=98784
36(y)^3=98784
(y)^3 = 98784/36=2744
y=cube root(2744)
y=14
therefore the numbers are 14 28 42