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)

1 answer

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.