Question

9 (x^2 +1/x^2) - 3 (x-1/x)-20=0

Answer 1

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Answer 2

Step-by-step explanation:

9(x2+1/x2) - 3(x-1/x) - 20 = 0

9(x-1/x)2 +2 - 3(x-1/x) - 20 = 0

let, x-1/x = m

9( m2 + 2) - 3 ( m) - 20 = 0

9m2 + 18 - 3m - 20 = 0

9m2 - 3m - 2 = 0

9m2 -6m + 3m -2 = 0

3m (3m - 2) +1(3m -2) = 0

3m+1 = 0 or 3m-2= 0

m = -1/3 or m = 2/3

x-1/x = -1/3 or x-1/x = 2/3

3x2+x-3= 0 or 3x2-2x-3=0

x= 1+/-√10/6 or x = -1 +/- √37/6