Question

find the x value 36 + 1/x = 3

Answer 1

SOLUTION

x6 - 36x3 - 1 = 0

x6 - 1 = 36x3

x3 - 1/x3 = 36

(x - 1/x)3 = x3 - 1/x3 - 3 × x × 1/x × (x - 1/x)

(x - 1/x)3 = 36 - 3(x - 1/x)

(x - 1/x)3 + 3(x - 1/x) - 36 = 0

(x - 1/x) = 3

Now,

(x + 1/x)2 = (x - 1/x)2 + 4 × x × 1/x

(x + 1/x)2 = 9 + 4 = 13

x + 1/x = √13