Question

Equation: 8 divided by displaystyle{left({x}^{2}+{x}+{1}right)}={1} Use crossing graphs method to solve the above equation. There are 2 solutions. Rou

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asked 2021-02-19
Equation: 8 divided by \(\displaystyle{\left({x}^{2}+{x}+{1}\right)}={1}\)
Use crossing graphs method to solve the above equation. There are 2 solutions. Round answers to 2 decimals. Provide smaller and larger value:
\(\displaystyle{x}={\left({s}{m}{a}{l}\le{r}{v}{a}{l}{u}{e}\right)}{x}={\left({l}{a}{r}\ge{r}{v}{a}{l}{u}{e}\right)}\)

Answers (1)

2021-02-20

Step 1
8 divided by \(\displaystyle{\left({x}^{2}+{x}+{1}\right)}={1}\)
This means,
\(\displaystyle{8}\text{/}{\left({x}^{2}+{x}+{1}\right)}={1}\)
Hence, \(\displaystyle{8}={x}^{2}+{x}+{1}\)
Step 2
Let's plot two graphs:
\(y = 8\)
and \(\displaystyle{y}={x}^{2}+{x}+{1}\)
image
There are two solutions (the points of intersection):
\(x =\ -3.19\) (smaller value)
\(x = 2.19\) ( larger value)

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