Question
Determine whether x=3
is the solution of 2x2+9−−−−−−√3=3
.
Enter 1 if x=3
is the solution.
Enter 2 if x=3
is not the solution.
(1 point)
Answers
Answered by
GPT-4o mini
To determine whether \( x = 3 \) is the solution of the equation \( 2x^2 + 9 - \sqrt{3} = 3 \), we can substitute \( x = 3 \) into the equation and see if both sides are equal.
Let's substitute \( x = 3 \):
\[
2(3)^2 + 9 - \sqrt{3} = 3
\]
Calculating \( 2(3)^2 \):
\[
2(9) = 18
\]
So, the left side of the equation becomes:
\[
18 + 9 - \sqrt{3} = 27 - \sqrt{3}
\]
Now we need to check if \( 27 - \sqrt{3} \) equals \( 3 \):
\[
27 - \sqrt{3} = 3
\]
To isolate \( \sqrt{3} \), we can rearrange this equation:
\[
27 - 3 = \sqrt{3}
\]
This simplifies to:
\[
24 = \sqrt{3}
\]
Since \( 24 \) is not equal to \( \sqrt{3} \), the equation does not hold true.
Thus, \( x = 3 \) is not a solution to the equation \( 2x^2 + 9 - \sqrt{3} = 3 \).
Enter **2** if \( x = 3 \) is not the solution.
Let's substitute \( x = 3 \):
\[
2(3)^2 + 9 - \sqrt{3} = 3
\]
Calculating \( 2(3)^2 \):
\[
2(9) = 18
\]
So, the left side of the equation becomes:
\[
18 + 9 - \sqrt{3} = 27 - \sqrt{3}
\]
Now we need to check if \( 27 - \sqrt{3} \) equals \( 3 \):
\[
27 - \sqrt{3} = 3
\]
To isolate \( \sqrt{3} \), we can rearrange this equation:
\[
27 - 3 = \sqrt{3}
\]
This simplifies to:
\[
24 = \sqrt{3}
\]
Since \( 24 \) is not equal to \( \sqrt{3} \), the equation does not hold true.
Thus, \( x = 3 \) is not a solution to the equation \( 2x^2 + 9 - \sqrt{3} = 3 \).
Enter **2** if \( x = 3 \) is not the solution.