Question

If x^2+1/x^2-5(x+1/x) +68/9=0, find x+1/x

Answer 1

Answer:

x + 1/x  = 5/3 or 10/3

Step-by-step explanation:

x²  + 1/x²   - 5(x + 1/x)  + 68/9 = 0

let say x + 1/x  = y  

Squaring both sides

=> x² + 1/x²  + 2x(1/x) = y²

=> x² + 1/x² = y² - 2

putting x + 1/x    & x² + 1/x² values

y² - 2  - 5y  + 68/9 = 0

multiplying by 9 noth sides

=> 9y² - 18 - 45y + 68 = 0

=> 9y² - 45y + 50 = 0

=> 9y² - 30y - 15y + 50 = 0

=> 3y(3y - 10) - 5(3y - 10) = 0

=> (3y - 5)(3y - 10) = 0

=> y = 5/3  or y = 10/3

=> x + 1/x  = 5/3 or 10/3