Exercise 3 | Wiskunde op Tilburg University

Solve

$(x^2+2)(x-1)>8(x-\frac{1}{4})$ .

Antwoord 1 correct

Correct

Antwoord 2 optie

$-2<x<3$ and

$x>3$

Antwoord 2 correct

Fout

Antwoord 3 optie

$\frac{1}{2}-\sqrt{6}<x<\frac{1}{2}+\sqrt{6}$ and

$x>\frac{1}{2}+\sqrt{6}$

Antwoord 3 correct

Fout

Antwoord 4 optie

$\frac{1}{2}-\sqrt{6}<x<0$ and

$x>\frac{1}{2}+\sqrt{6}$

Antwoord 4 correct

Fout

Antwoord 1 optie

$-2<x<0$ and

$x>3$

Antwoord 1 feedback

Correct:

$\begin{align*} (x^2+2)(x-1)=8(x-\frac{1}{4}) & \Leftrightarrow x^3+2x-x^2-2=8x-2\\ & \Leftrightarrow x^3-x^2-6x=0\\ & \Leftrightarrow x(x^2-x-6)=0\\ & \Leftrightarrow x(x-3)(x+2)=0\\ & \Leftrightarrow x=3 \mbox{ of } x=0 \mbox{ or } x=-2. \end{align*}$

Via a sign chart we find

$-2<x<0$ and

$x>3$ .

Go on.

Antwoord 2 feedback

Wrong: Do not forget

$x=0$ as a solution of the corresponding equation.

Try again.

Antwoord 3 feedback

Wrong:

$(-1)^2\neq -1$ .

Try again.

Antwoord 4 feedback

Wrong:

$(-1)^2\neq -1$ .

Try again.