Exercise 4 | Wiskunde op Tilburg University

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.

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.

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.

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.