I assume you mean x - (1/x) and not (x-1)/x, and that 77/12(x - 1/x) means (77/12)[x - (1/x)]. If not, please write your equation in an unambiguous manner, using more parentheses.
Treat (x - 1/x) as a new variable y, and solve the equation
y^2 - (77/12) y + 10 = 0
That cannot be factored easily, so use the quadratic formula to get the two possible value os y. Once you have a number for y, solve the equation
x - 1/x = y to get x
That will require solveing a different quadratic equation. There should be four answers, but no all may be real.
how would i factor
(x - 1/x)^2 - 77/12(x - 1/x) + 10 = 0
2 answers
sorry about that. yes i meant x - (1/x).
so i subbed in y for [x - (1/2)]^2, and used the quadratic formula.
i have y = 77/12 +- root of (169/44) all divided by 2.
i'm not sure where to go with this and how i should solve for x. please help
so i subbed in y for [x - (1/2)]^2, and used the quadratic formula.
i have y = 77/12 +- root of (169/44) all divided by 2.
i'm not sure where to go with this and how i should solve for x. please help