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)

Answer 1

To determine whether \( x = 3 \) is a solution to the equation

\[
2x^2 + \sqrt{9} \cdot 3 = 3,
\]

let's substitute \( x = 3 \) into the equation.

First, calculate \( 2x^2 \) when \( x = 3 \):

\[
2(3^2) = 2(9) = 18.
\]

Next, calculate \( \sqrt{9} \cdot 3 \):

\[
\sqrt{9} = 3 \quad \text{so} \quad 3 \cdot 3 = 9.
\]

Now, combine these results:

\[
18 + 9 = 27.
\]

Now we need to check if this equals 3:

\[
27 \neq 3.
\]

Since substituting \( x = 3 \) into the equation did not satisfy it, we conclude that \( x = 3 \) is not a solution.

Therefore, the answer is:

2 (x=3 is not the solution).