Question

if [x3+1/x3] = 52, the value of
x+1/x
(A) 4
(C) 6
(B) 3
(D) 13​

Answer 1

Answer:

x + 1/x = 4

Step-by-step explanation:

x^3 + 1/x^3 = 52

(x + 1/x)^3 - 3(x + 1/x) = 52

Let x + 1/x be y

y^3 - 3y - 52 = 0

y^3 - 4y^2 + 4y^2 - 16y + 13y - 52 = 0

y^2 (y - 4) + 4y (y - 4) + 13(y - 4) = 0

(y - 4) (y^2 + 4y + 13) = 0

y = 4. So x + 1/x = 4