problem_id int64 0 3.39k | problem stringlengths 20 2.22k | label stringclasses 154
values | level stringclasses 5
values | type stringclasses 4
values | prompt listlengths 2 2 | completion listlengths 1 1 |
|---|---|---|---|---|---|---|
3,389 | Solve
\[(x^3 + 3x^2 \sqrt{2} + 6x + 2 \sqrt{2}) + (x + \sqrt{2}) = 0.\]Enter all the solutions, separated by commas. | 2 | Level 4 | Intermediate Algebra | [
{
"role": "system",
"content": "Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\\boxed{{ANSWER}}$ where ANSWER is just the final number or expression that solves the problem. Think step by step bef... | [
{
"role": "assistant",
"content": "We are asked: \"Determine the number of pairs (a,b) of real numbers such that 10, a, b, ab is an arithmetic progression.\" We need to solve using the method: Direct substitution from linear relation.\n\nInterpretation: The four numbers 10, a, b, ab are in arithmetic progre... |
3,389 | Solve
\[(x^3 + 3x^2 \sqrt{2} + 6x + 2 \sqrt{2}) + (x + \sqrt{2}) = 0.\]Enter all the solutions, separated by commas. | 2 | Level 4 | Intermediate Algebra | [
{
"role": "system",
"content": "Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\\boxed{{ANSWER}}$ where ANSWER is just the final number or expression that solves the problem. Think step by step bef... | [
{
"role": "assistant",
"content": "We are asked: \"Determine the number of pairs (a,b) of real numbers such that 10, a, b, ab is an arithmetic progression.\" We need to find number of real pairs (a,b). Use method: Second-order recurrence relation.\n\nInterpretation: The four numbers are in arithmetic progre... |
3,389 | Solve
\[(x^3 + 3x^2 \sqrt{2} + 6x + 2 \sqrt{2}) + (x + \sqrt{2}) = 0.\]Enter all the solutions, separated by commas. | 2 | Level 4 | Intermediate Algebra | [
{
"role": "system",
"content": "Solve the following math problem efficiently and clearly. The last line of your response should be of the following format: 'Therefore, the final answer is: $\\boxed{{ANSWER}}$ where ANSWER is just the final number or expression that solves the problem. Think step by step bef... | [
{
"role": "assistant",
"content": "We are asked: \"Determine the number of pairs (a,b) of real numbers such that 10, a, b, ab is an arithmetic progression.\" So the sequence: 10, a, b, ab are four terms in arithmetic progression. So there exists common difference d such that:\n\na = 10 + d\nb = a + d = 10 +... |
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