SOLUTION: 30(x^2+1/x^2)-77(x-1/x)-12=0

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: 30(x^2+1/x^2)-77(x-1/x)-12=0      Log On


   

Question 877417: 30(x^2+1/x^2)-77(x-1/x)-12=0
Answer by Edwin McCravy(20054) About Me  (Show Source):
You can put this solution on YOUR website!
30(x^2+1/x^2)-77(x-1/x)-12=0
30%28x%5E2%2B1%2Fx%5E2%29-77%28x%2B1%2Fx%29-12%22%22=%22%22%220%22
Let u%22%22=%22%22x%2B1%2Fx

Then

    u%5E2%22%22=%22%22%28x%2B1%2Fx%29%5E2%22%22=%22%22x%5E2%2B2%2B1%2Fx%5E2

    u%5E2%22%22=%22%22x%5E2%2B1%2Fx%5E2%2B2

    u%5E2-2%22%22=%22%22x%5E2%2B1%2Fx

So substitute u%5E2-2 for x%5E2%2B1%2Fx
and u for x%2B1%2Fx

30%28u%5E2-2%29-77u-12%22%22=%22%22%220%22

30u%5E2-60-77u-12%22%22=%22%22%220%22

30u%5E2-77u-72%22%22=%22%22%220%22

Use the quadratic formula, get

((u=(77 +- sqrt(14569))/60}}}


x%2B1%2Fx%22%22=%22%22%2877+%2B-+sqrt%2814569%29%29%2F60

Solve that and get

x+=+1%2F120+%2877-sqrt%2814569%29+%2B-+i%2Asqrt%282%2877sqrt%2814569%29-3049%29%29%29

It's too complicated.  I believe you may have copied something wrong.

This has four complicated complex roots and I don't believe your
teacher would have given you such a laborious problem.
Edwin