Solve for x: 4(x-1/x)^2 - 4(x+1/x) +1=0, x not equal to 0.
Nikti:
are u sure that there was( x-1/x) in the first one and (x+1/x) on the second one
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4(x - 1/x)^2 -4(x +1/x) +1 =0
we know ,
( x -1/x)^2 =(x +1/x)^2 -4
4{(x+1/x)^2 -4} -4(x + 1/x) +1 =0
4(x + 1/x)^2 -4( x +1/x) -15 =0
let (x + 1/x) = r
4r^2 -4r -15 =0
4r^2 -10r +6r -15 =0
2r(2r -5) +3(2r -5) =0
(2r +3)(2r -5) = 0
r = -3/2 and 5/2
x + 1/x = 5/2
2x^2 +2 -5x =0
2x^2 -5x +2 =0
use quadratic equation formula ,
x ={ 5 +_√9}/4 =2 , 1/2
also , x + 1/x = -3/2
2x^2 +3x +2 =0
no real solution possible to this
so, answer is x = 2, 1/2
we know ,
( x -1/x)^2 =(x +1/x)^2 -4
4{(x+1/x)^2 -4} -4(x + 1/x) +1 =0
4(x + 1/x)^2 -4( x +1/x) -15 =0
let (x + 1/x) = r
4r^2 -4r -15 =0
4r^2 -10r +6r -15 =0
2r(2r -5) +3(2r -5) =0
(2r +3)(2r -5) = 0
r = -3/2 and 5/2
x + 1/x = 5/2
2x^2 +2 -5x =0
2x^2 -5x +2 =0
use quadratic equation formula ,
x ={ 5 +_√9}/4 =2 , 1/2
also , x + 1/x = -3/2
2x^2 +3x +2 =0
no real solution possible to this
so, answer is x = 2, 1/2
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