Answer :
To solve the equation [tex]\( x^2 = 9 \)[/tex], we need to determine which of the given options, if any, satisfy this equation. Let's evaluate each option one by one:
A. [tex]\( x = 0 \)[/tex]
- Calculate [tex]\( 0^2 \)[/tex], which equals 0.
- Since 0 is not equal to 9, [tex]\( x = 0 \)[/tex] is not a solution.
B. [tex]\( x = 81 \)[/tex]
- Calculate [tex]\( 81^2 \)[/tex], which equals 6561.
- Since 6561 is not equal to 9, [tex]\( x = 81 \)[/tex] is not a solution.
C. [tex]\( x = 3 \)[/tex]
- Calculate [tex]\( 3^2 \)[/tex], which equals 9.
- Since 9 equals 9, [tex]\( x = 3 \)[/tex] is a solution.
D. [tex]\( x = -3 \)[/tex]
- Calculate [tex]\((-3)^2\)[/tex], which also equals 9.
- Since 9 equals 9, [tex]\( x = -3 \)[/tex] is a solution.
E. [tex]\( x = 81 \)[/tex]
- This option is repeated, and as previously concluded, [tex]\( x = 81 \)[/tex] is not a solution.
F. None
- Since we have already identified solutions (3 and -3), this option is not correct.
Thus, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( x^2 = 9 \)[/tex] are [tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex]. The correct solutions are C and D.
A. [tex]\( x = 0 \)[/tex]
- Calculate [tex]\( 0^2 \)[/tex], which equals 0.
- Since 0 is not equal to 9, [tex]\( x = 0 \)[/tex] is not a solution.
B. [tex]\( x = 81 \)[/tex]
- Calculate [tex]\( 81^2 \)[/tex], which equals 6561.
- Since 6561 is not equal to 9, [tex]\( x = 81 \)[/tex] is not a solution.
C. [tex]\( x = 3 \)[/tex]
- Calculate [tex]\( 3^2 \)[/tex], which equals 9.
- Since 9 equals 9, [tex]\( x = 3 \)[/tex] is a solution.
D. [tex]\( x = -3 \)[/tex]
- Calculate [tex]\((-3)^2\)[/tex], which also equals 9.
- Since 9 equals 9, [tex]\( x = -3 \)[/tex] is a solution.
E. [tex]\( x = 81 \)[/tex]
- This option is repeated, and as previously concluded, [tex]\( x = 81 \)[/tex] is not a solution.
F. None
- Since we have already identified solutions (3 and -3), this option is not correct.
Thus, the values of [tex]\( x \)[/tex] that satisfy the equation [tex]\( x^2 = 9 \)[/tex] are [tex]\( x = 3 \)[/tex] and [tex]\( x = -3 \)[/tex]. The correct solutions are C and D.
