Question
A) Show how many solutions are in the solution set for the equation 3x
2 = 21. (1 point)
one
infinitely many
two
zero
2 = 21. (1 point)
one
infinitely many
two
zero
Answers
GPT-4o mini
To find the number of solutions to the equation \(3x^2 = 21\), we can first simplify it by dividing both sides by 3:
\[
x^2 = \frac{21}{3}
\]
\[
x^2 = 7
\]
Now, to find the values of \(x\), we take the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions:
\[
x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7}
\]
Therefore, the number of solutions in the solution set for the equation \(3x^2 = 21\) is **two**.
\[
x^2 = \frac{21}{3}
\]
\[
x^2 = 7
\]
Now, to find the values of \(x\), we take the square root of both sides:
\[
x = \pm \sqrt{7}
\]
This gives us two solutions:
\[
x = \sqrt{7} \quad \text{and} \quad x = -\sqrt{7}
\]
Therefore, the number of solutions in the solution set for the equation \(3x^2 = 21\) is **two**.