Question

Using properties of proportion,solve the equation:-
x^3+3x/3x^2+1=341/91

Answer 1

Step-by-step explanation:

Sol: Given (x3+3x) / (3x2+1) = 341 / 91. Apply the componendo and dividendo ⇒ (x3+3x) + (3x2+1) / (x3+3x) - (3x2+1) = (341 + 91) / (341 - 91). ⇒ (x3 + 3x2 + 3x + 1) / (x3- 3x2 +3x -1) = (341 + 91) / (341 - 91). ⇒ (x + 1)3 / (x - 1)3 = 432 / 250. ⇒ (x + 1)3 / (x - 1)3 = 216 / 125 . ⇒ (x + 1)3 / (x - 1)3 = 63 / 53 . ⇒ (x + 1) / (x - 1) = 6 / 5 .(again apply the componendo and dividendo) ⇒ (x + 1) + (x - 1) /(x + 1) - (x - 1) = (6 + 5) / (6 - 5) ⇒ 2x / 2 = 11 / 1 ∴ x = 11.