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 = ?

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asked 2020-10-28

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asked 2021-02-19

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asked 2020-11-23

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asked 2021-01-02

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asked 2021-02-06

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asked 2021-01-31

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asked 2021-02-20

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asked 2021-03-12

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asked 2021-02-05

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asked 2020-10-28

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Answer 1

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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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 = ?

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