SOLUTION: Please solve the equation y^2-6y+8=0 Hence find the roots of the equation (x+1/x)^2 -6(x+1/x)+8=0 x is the denominator This is a tough one

Question 365991: Please solve the equation
y^2-6y+8=0

Hence find the roots of the equation
(x+1/x)^2 -6(x+1/x)+8=0 x is the denominator
This is a tough one. I tried to do it but it's the first time I've seen this.
Answer by amoresroy(361) (Show Source): You can put this solution on YOUR website!
Please solve the equation
y^2-6y+8=0
By factoring, you get
(y-2) (y-4) = 0
So you have 2 values for y
y = 2
y = 4
Hence find the roots of the equation
(x+1/x)^2 -6(x+1/x)+8=0 x is the denominator
let y = x+1/x
So the equation is equal to
y^2-6y+8=0
where
y=2
y=4
Using y=2, then
2 = x+1/x
multiply both sides by x
2x = x^2+1
subtract 2x to both sides
0 = x^2-2x+1
By factoring, you get
(x-1) (x-1) = 0
So x = 1
Using y=4, then
4 = x+1/x
multiply both sides by x
4x = x^2+1
subtract 4x to both sides
0 = x^2-4x+1
Solve using quadratic formula
x = [4 +/- (16-4)^.5]/2
= [4 +/- 2(3)^.5] /2

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