Solve the equation. x^{3}-8=x-2

jernplate8 2021-09-29 Answered
Solve the equation.
\(\displaystyle{x}^{{{3}}}-{8}={x}-{2}\)

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more

Plainmath recommends

  • Ask your own question for free.
  • Get a detailed answer even on the hardest topics.
  • Ask an expert for a step-by-step guidance to learn to do it yourself.
Ask Question

Expert Answer

cyhuddwyr9
Answered 2021-09-30 Author has 11209 answers
Step 1
Consider the given equation.
\(\displaystyle{x}^{{{3}}}-{8}={x}-{2}\)
Step 2
On solving above equation,
\(\displaystyle{x}^{{{3}}}-{8}-{x}+{2}={0}\)
\(\displaystyle{x}^{{{3}}}-{x}-{6}={0}\)
Step 3
Since, the one factor of this equation is (x – 2), so
\(\displaystyle\Rightarrow{\frac{{{x}^{{{3}}}-{x}-{6}}}{{{x}-{2}}}}\)
\(\displaystyle\Rightarrow{x}^{{{2}}}+{2}{x}+{3}\)
Step 4
Now, solving the above quadratic equation
\(\displaystyle{x}^{{{2}}}+{2}{x}+{3}={0}\)
Step 5
Formula used:
\(\displaystyle{x}={\frac{{-{b}\pm\sqrt{{{b}^{{{2}}}-{4}{a}{c}}}}}{{{2}{a}}}}\)
Step 6
Therefore,
\(\displaystyle{x}={\frac{{-{2}\pm\sqrt{{{2}^{{{2}}}-{4}\times{1}\times{3}}}}}{{{2}\times{1}}}}\)
\(\displaystyle{x}={\frac{{-{2}\pm\sqrt{{{4}-{12}}}}}{{{2}}}}\)
\(\displaystyle{x}={\frac{{-{2}\pm\sqrt{{-{8}}}}}{{{2}}}}\)
\(\displaystyle{x}={\frac{{-{2}\pm{2}{i}\sqrt{{{2}}}}}{{{2}}}}\)
\(\displaystyle{x}=-{1}\pm{i}\sqrt{{{2}}}\)
Step 7
Answer: The factors of the equation is equal to
\(\displaystyle{2},-{1}+{i}\sqrt{{{2}}},-{1}-{i}\sqrt{{{2}}}\)
Have a similar question?
Ask An Expert
21
 

Expert Community at Your Service

  • Live experts 24/7
  • Questions are typically answered in as fast as 30 minutes
  • Personalized clear answers
Learn more
...