# Solve the equation graphically in the given interval. State each answer rounded to two decimals. displaystyle{x}^{{frac{1}{{3}}}}-{x}={0},{left[-{3},{3}right]} x = ?

Question
Decimals
Solve the equation graphically in the given interval. State each answer rounded to two decimals.
$$\displaystyle{x}^{{\frac{1}{{3}}}}-{x}={0},{\left[-{3},{3}\right]}$$
$$x = ?$$

2020-10-28
To find: Solve for x in the interval $$\displaystyle{\left[-{3},{3}\right]}$$ graphically,
$$\displaystyle{x}^{{\frac{1}{{3}}}}-{x}={0}$$
$$\displaystyle\Rightarrow{x}^{{\frac{1}{{3}}}}={x}$$
In order to solve graphically, we plot say $$\displaystyle{y}={x}^{{\frac{1}{{3}}}}\ \text{and}\ z = x$$ and find the points where the two graphs intersect.

From the graph it is clear that the graphs intersect at three points. That is, $$x =\ -1,\ x = 0\ \text{and}\ x = 1$$ which are the solution for the given equation.
Hence, solution set is $$\displaystyle{\left\lbrace-{1},{0},{1}\right\rbrace}.$$

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