Question

Fool's problem of the day,

If \(2x^4+x^3-11x^2+x+2=0\), what are the values of \(x+\frac1x\)?

Answer 1

\[x \approx 2.1085\]\[x \approx -2.6085\]

x+(1/x)
=2.582770809
=-2.991862085

Answer 2

Where's the fun in that?

Answer 3

Well, we are suppose to solve it without any electronic aid.

Answer 4

lol

Answer 5

\[2x^4+x^3-11x^2+x+2=0/:x^2\]\[2x^2+x-11+\frac{1}{x}+\frac{2}{x^2}=0\]\[2\left(x^2+\frac{1}{x^2}\right)+x+\frac{1}{x}-11=0\]\[x+\frac{1}{x}=y\quad,\quad x^2+\frac{1}{x^2}=y^2-2\]\[2\left(y^2-2\right)+y-11=0\]\[2y^2+y-15=0\]\[(y+3)(2y-5)=0\]\[y=-3\quad\vee\quad y=5/2\]

Answer 6

Well done nikvist.