SOLUTION: how would you solve ((1/x)-(x/2))((2/x)-(x))=(1/2) When i tried to solve it i got stuck when trying to factor it.

Question 579762: how would you solve ((1/x)-(x/2))((2/x)-(x))=(1/2)
When i tried to solve it i got stuck when trying to factor it.
Answer by unlockmath(1688) (Show Source): You can put this solution on YOUR website!
Hello,
This ((1/x)-(x/2))((2/x)-(x))=(1/2) we can do as follows:
Distribute to get:
2/x^2-2+x^2/2=1/2
Eliminate the denominators by multiplying by 2x^2 to get:
4-4x^2+x^4=x^2
Rewritten as:
x^4-5x^2+4=0
Let u equal x^2:
u^2-5u+4=0
factor as:
(u-4)(u-1)=0
Solve for u to get:
u=4
u=1
Replace u with x^2
x^2=4
square root both sides:
x=+-2
Solve the other one:
x^2=1
Sq rt:
x=+-1
Check these out in the original equation-they should be fine.
Make sense?
RJ
www.math-unlock.com
RELATED QUESTIONS
How would you solve... ((1/x)^2-(x)^2)/((1/x)+(x))=(3/2) When i tried solving it i got (answered by scott8148)

Good afternoon, Can someone please help me solve this question? Thank you in advance... (answered by Fombitz)

1/x + 2/x = 6 It asks that i solve the equation. I got it down to 3/x = 6 and that... (answered by Mathtut)

I am trying to solve the quadratic equation 3x-12. When I factor out the binomial I get... (answered by richwmiller)

ax^2+(a+1)x+(a-1) = 0 I need to solve this equation for x. I've been trying to factor... (answered by richard1234,josgarithmetic)

Hi, I am trying to solve: x(x-3)=21 I tried the distributive property and got... (answered by stanbon)

I have the following inequality, trying to solve it: 1/2 - x > x/3 + 1/4 (answered by lwsshak3)

I would appreciat help with this one. Thank you (1-x)^2=9 I think that I need to set... (answered by Alan3354)

how do you solve this ?: 5/6X - 1/3 = 5/12 I tried solving it and got down to the final (answered by rfer)