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Example 1
If $\dfrac{2}{\sqrt[3]{|x|+2}}=1$, then $|x|=$?
- $6$
- $7$
- $8$
- $9$
- $10$ and $1$
Solution
- Rewrite the given equation as follows $\dfrac{2}{\sqrt[3]{|x|+2}}=\dfrac{1}{1}$ and cross multiply to obtain
$2 = \sqrt[3]{|x|+2}$
- Because of the cube root we rais both sides to the power 3
$(2)^3 = (\sqrt[3]{|x|+2})^3$
- Use the rule $(\sqrt[3]x)^3=x$ to simplify the right side
$8 = |x|+2$
- Solve for |x|.
$|x|=6$
Answer A
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