2014/060) using properties of proportions solve ( x^3 + 3x )/341 = (3x^2 + 1)/91

we have

(x^3 + 3x)/341 = (3x^2 + 1)/91

which is same as
(x^3 + 3x)/(3x^2 + 1)= 341/91

using componendo dividendo we have
(x^3+3x+3x^2+1)/(x^3+3x-3x^2-1) = (341+91)/(341-91)

or (x+1)^3/(x-1)^3 = (216)/125

hence (x+1)/(x-1) = 6/5

using componendo dividendo we have

(2x/2) = (11/1) or x= 11