### Math Notes

Subjects

#### High School Mathematics Solutions

##### Topics || Problems

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