Find the sum of the distinct roots of \( (x+\frac{2}{x})^2-6(x+\frac{2}{x})+9 = 0\)

Solution

• \( ((x+\frac{2}{x})-3 )^2= 0\)

• \( x + \frac{2}{x}-3 = 0\)

• \( x^2 -3x + 2 = 0 \)

• \(x_1 = \frac{--3-\sqrt{9-4(2)}}{2} = 2\)

• \(x_1 = \frac{--3+\sqrt{9-4(2)}}{2} =1\)

• Sum = 3