jernplate8

2021-09-29

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

cyhuddwyr9

Expert

Step 1
Consider the given equation.
${x}^{3}-8=x-2$
Step 2
On solving above equation,
${x}^{3}-8-x+2=0$
${x}^{3}-x-6=0$
Step 3
Since, the one factor of this equation is (x – 2), so
$⇒\frac{{x}^{3}-x-6}{x-2}$
$⇒{x}^{2}+2x+3$
Step 4
Now, solving the above quadratic equation
${x}^{2}+2x+3=0$
Step 5
Formula used:
$x=\frac{-b±\sqrt{{b}^{2}-4ac}}{2a}$
Step 6
Therefore,
$x=\frac{-2±\sqrt{{2}^{2}-4×1×3}}{2×1}$
$x=\frac{-2±\sqrt{4-12}}{2}$
$x=\frac{-2±\sqrt{-8}}{2}$
$x=\frac{-2±2i\sqrt{2}}{2}$
$x=-1±i\sqrt{2}$
Step 7
Answer: The factors of the equation is equal to
$2,-1+i\sqrt{2},-1-i\sqrt{2}$

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