Question

question 39 points 1

solve: \\(x^2 - 4 = 0\\).

• 2 and 2
• -2 and 2

Explanation:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
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"concepts_used": [
"Quadratic Equations",
"Difference of Squares"
],
"new_concepts": [],
"current_concepts": [
"Quadratic Equations",
"Difference of Squares"
]
}
</pre_analysis>

<reasoning>

Isolate the quadratic term

\[
x^2 = 4
\]

Apply the square root property

\[
x = \pm\sqrt{4}
\]

Simplify the roots

\[
x = 2 \quad \text{or} \quad x = -2
\]
</reasoning>

<answer>
<mcq-option>2 and 2</mcq-option>
<mcq-correct>-2 and 2</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>

Answer:

<pre_analysis>
{
"quality": "clear",
"question_count": 1,
"skills_matched": [
"step_cot",
"multiple_choice_formatter",
"explain_then_answer",
"quick"
],
"needs_drawing": false,
"concepts_used": [
"Quadratic Equations",
"Difference of Squares"
],
"new_concepts": [],
"current_concepts": [
"Quadratic Equations",
"Difference of Squares"
]
}
</pre_analysis>

<reasoning>

Isolate the quadratic term

\[
x^2 = 4
\]

Apply the square root property

\[
x = \pm\sqrt{4}
\]

Simplify the roots

\[
x = 2 \quad \text{or} \quad x = -2
\]
</reasoning>

<answer>
<mcq-option>2 and 2</mcq-option>
<mcq-correct>-2 and 2</mcq-correct>
</answer>

<post_analysis>
{
"subject": "Mathematics",
"question_type": "Multiple Choice",
"knowledge_point": [
"Mathematics",
"Algebra",
"Quadratic Equations"
]
}
</post_analysis>