SOLUTION: The question is solve: {{{(x-2/x)^2+4(x-2/x)=5}}} The closet I have come to solving this is probably way off. I have ended up with: {{{x^4=9}}} and {{{x^4-4x+4/x^2+4x-8/

Algebra ->  Quadratic Equations and Parabolas  -> Quadratic Equations Lessons  -> Quadratic Equation Lesson -> SOLUTION: The question is solve: {{{(x-2/x)^2+4(x-2/x)=5}}} The closet I have come to solving this is probably way off. I have ended up with: {{{x^4=9}}} and {{{x^4-4x+4/x^2+4x-8/      Log On


   

Question 156760: The question is solve:
%28x-2%2Fx%29%5E2%2B4%28x-2%2Fx%29=5
The closet I have come to solving this is probably way off.
I have ended up with:
x%5E4=9 and
x%5E4-4x%2B4%2Fx%5E2%2B4x-8%2Fx=5
Any help would be greatly appreciated.
Thanks to all the online tutors out there...
Bill W

Answer by edjones(8007) About Me  (Show Source):
You can put this solution on YOUR website!
%28x-2%2Fx%29%5E2%2B4%28x-2%2Fx%29=5
Let a=x-(2/x)
a^2+4a=5
a^2+4a-5=0
(a+5)(a-1)=0
a=-5, a=1
.
x-(2/x)=-5
x^2-2=-5x mult each side by x
x^2+5x-2=0
x^2+5x =2
x^2+5x+25/4=2+25/4 completing the square.
(x+(5/2))^2=33/4
x+(5/2)=+-sqrt(33)/2
x=(-5+sqrt(33))/2, x=(-5-sqrt(33))/2
.
x-(2/x)=1
x^2-2=x
x^2-x-2=0
(x-2)(x+1)=0
x=2, x=-1
.
Ed