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.
(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.
Try again.
Antwoord 3 feedback
Wrong: $(-1)^2\neq -1$.
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Try again.
Antwoord 4 feedback
Wrong: $(-1)^2\neq -1$.
Try again.
Try again.