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Find the real solution(s) of the following equation.

[tex]\[ p^3 = 125 \][/tex]

Choose all answers that apply:

A. [tex]\( p = 3 \)[/tex]
B. [tex]\( p = -3 \)[/tex]
C. [tex]\( p = 6 \)[/tex]
D. [tex]\( p = -6 \)[/tex]
E. None of the above

Sagot :

GinnyAnsweridn
To solve the equation [tex]\( p^3 = 125 \)[/tex], follow these steps:

1. Identify the equation: We begin with the equation [tex]\( p^3 = 125 \)[/tex].

2. Express 125 as a power of a simpler number:
[tex]\[ 125 = 5^3 \][/tex]

3. Set up the equation with equivalent powers:
[tex]\[ p^3 = 5^3 \][/tex]

4. Since the powers are equal, the bases must also be equal:
[tex]\[ p = 5 \][/tex]

So the real solution to the equation [tex]\( p^3 = 125 \)[/tex] is [tex]\( p = 5 \)[/tex].

Now, let us analyze the provided choices:
- (A) [tex]\( p = 3 \)[/tex]
- (B) [tex]\( p = -3 \)[/tex]
- (C) [tex]\( p = 6 \)[/tex]
- (D) [tex]\( p = -6 \)[/tex]
- (E) None of the above

Comparing each choice with our solution [tex]\( p = 5 \)[/tex]:

- [tex]\( p = 3 \)[/tex] (A): [tex]\( 3^3 = 27 \)[/tex], not equal to 125.
- [tex]\( p = -3 \)[/tex] (B): [tex]\( (-3)^3 = -27 \)[/tex], not equal to 125.
- [tex]\( p = 6 \)[/tex] (C): [tex]\( 6^3 = 216 \)[/tex], not equal to 125.
- [tex]\( p = -6 \)[/tex] (D): [tex]\( (-6)^3 = -216 \)[/tex], not equal to 125.

Since none of these choices are equal to 125, the correct answer must be:
- (E) None of the above

Therefore, the correct answer is:
(E) None of the above
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