MHB Where should the values be placed to correctly solve for x?

[06Rousher]

"x=2+1/x"

What I got is this: -x^2=2 then x^2=-2, then x=4

 

[lfdahl]

Re: Wanting to make I got this correct

x = 2 + 1/x

To find x, I think it would be appropriate to multiply both sides with x, and solve the quadratic equation.

 

[06Rousher]

Re: Wanting to make I got this correct

x = 2 + 1/x

To find x, I think it would be appropriate to multiply both sides with x, and solve the quadratic equation

So x^2-2x-1? Doesn't seem like that would be solvable.

I got 2.41 for x

 

[lfdahl]

Re: Wanting to make I got this correct

Why not? You did solve the equation:

x^2-2x-1 = 0 --> x = 1+/- sqrt(2)

 

[06Rousher]

Re: Wanting to make I got this correct

Why not? You did solve the equation:

x^2-2x-1 = 0 --> x = 1+/- sqrt(2)

How did you get to x=1 +/- sqrt(2)?

 

[lfdahl]

Re: Wanting to make I got this correct

The quadratic equation: x²- 2x - 1 = 0

Discriminant: D = (-2)²-4(1)(-1) = 8

The two solutions:

x1 = (2 + sqrt(8))/2 and x2 = (2 - sqrt(8))/2

or

x1 = 1 + sqrt(2) and x2 = 1 - sqrt(2)

In general for solving a quadratic equation:

\[ax^{2}+bx+c=0 \\\\D = b^{2}-4ac \\\\x = \frac{-b\pm \sqrt{D}}{2a}\]

 

[06Rousher]

Re: Wanting to make I got this correct

Thank you so much

That last part really helped me understand it, I was having trouble on where to place the values