Solve $12\cdot (3x^2)^3=(6x^4)^2(2x^2)^{-2}$.
Antwoord 1 correct
Correct
Antwoord 2 optie
$x=\frac{1}{6}$, $x=-\frac{1}{6}$ or $x=0$.
Antwoord 2 correct
Fout
Antwoord 3 optie
$x=\sqrt{\frac{1}{3}}$, $x=-\sqrt{\frac{1}{3}}$ or $x=0$.
Antwoord 3 correct
Fout
Antwoord 4 optie
$x=\sqrt{\frac{1}{3}}$ or $x=-\sqrt{\frac{1}{3}}$.
Antwoord 4 correct
Fout
Antwoord 1 optie
$x=\frac{1}{6}$ or $x=-\frac{1}{6}$.
Antwoord 1 feedback
Correct: $$\begin{align*}
12\cdot (3x^2)^3=(6x^4)^2(2x^2)^{-2} & \Leftrightarrow 12\cdot 3^3 \cdot (x^2)^3=6^2\cdot (x^4)^2\cdot 2^{-2}\cdot(x^2)^{-2}\\
& \Leftrightarrow 324 \cdot (x^2)^3=9\cdot (x^4)^2\cdot(x^2)^{-2}\\
& \Leftrightarrow 324 \cdot x^6=9\cdot x^8 \cdot x^{-4}\\
& \Leftrightarrow 324 \cdot x^6=9\cdot x^4\\
& \Leftrightarrow x^2=\frac{1}{36}\\
& \Leftrightarrow x=\frac{1}{6} \mbox{ or } x=-\frac{1}{6}.
\end{align*}$$
Go on.
12\cdot (3x^2)^3=(6x^4)^2(2x^2)^{-2} & \Leftrightarrow 12\cdot 3^3 \cdot (x^2)^3=6^2\cdot (x^4)^2\cdot 2^{-2}\cdot(x^2)^{-2}\\
& \Leftrightarrow 324 \cdot (x^2)^3=9\cdot (x^4)^2\cdot(x^2)^{-2}\\
& \Leftrightarrow 324 \cdot x^6=9\cdot x^8 \cdot x^{-4}\\
& \Leftrightarrow 324 \cdot x^6=9\cdot x^4\\
& \Leftrightarrow x^2=\frac{1}{36}\\
& \Leftrightarrow x=\frac{1}{6} \mbox{ or } x=-\frac{1}{6}.
\end{align*}$$
Go on.
Antwoord 2 feedback
Wrong: $x=0$ is not part of the domain of this equation: $(2\cdot 0^2)^{-2}$ has no value.
Try again.
Try again.
Antwoord 3 feedback
Wrong: $x=0$ is not part of the domain of this equation: $(2\cdot 0^2)^{-2}$ has no value.
Try again.
Try again.
Antwoord 4 feedback
Wrong: $12\cdot (3x^2)^3=(6x^4)^2(2x^2)^{-2}$ cannot be rewritten as $12\cdot 3 \cdot (x^2)^3=6\cdot (x^4)^2\cdot 2\cdot(x^2)^{-2}$.
See Properties power functions.
See Properties power functions.