Find all real solutions of the equation. $7 ( x - 1 ) ^ { 3 } - 2401 = 0$
A) No real solution
B) $- 8$
C) $8$
D) $\pm 8$
E) $\pm 7$

Question

Quizplus · Accepted Answer

First, we can simplify the equation by dividing both sides by 7:

$$(x-1)^3=343$$

Next, we can take the cube root of both sides:

$$x-1=7$$ or $$x-1=-7$$

Solving for $x$ in each case gives us:

$$x=8$$ or $$x=-6$$

However, we need to check if $x=-6$ is really a solution, since taking the cube root of a negative number involves complex numbers. Plugging $x=-6$ into the original equation gives:

$$7(-6-1)^3-2401 = -7^3-2401=-2744
eq 0$$

Since $x=-6$ is not a solution, the only real solution is $x=8$, so the answer is C) 8.

Find All Real Solutions of the Equation 7(x−1)3−2401=07 ( x - 1 ) ^ { 3 } - 2401 = 07(x−1)3−2401=0

Find All Real Solutions of the Equation $7 ( x - 1 ) ^ { 3 } - 2401 = 0$