__source_repo string | problem string | generations sequence | solution string | answer string | problem_type string | question_type string | source string | uuid string | is_reasoning_complete sequence | correctness_math_verify sequence | correctness_llama sequence | finish_reasons sequence | correctness_count int64 | messages list | __orig_idx int64 | __chunk_idx int64 | generations__chunked string | eval_prompt list | eval_steps list | steps_word_count int64 | trace_word_count int64 | word_count_diff int64 |
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open-r1/OpenR1-Math-220k | 3. [4 points] Solve the equation $\left(\frac{x}{2 \sqrt{2}}+\frac{5 \sqrt{2}}{2}\right) \sqrt{x^{3}-64 x+200}=x^{2}+6 x-40$. | [
"<think>\nOkay, so I need to solve this equation: \n\n\\[\n\\left(\\frac{x}{2 \\sqrt{2}}+\\frac{5 \\sqrt{2}}{2}\\right) \\sqrt{x^{3}-64 x+200} = x^{2}+6 x-40\n\\]\n\nHmm, that looks a bit intimidating with the square root and the cubic inside it. Let me take it step by step.\n\nFirst, maybe I should check if there ... | Answer: $6, \sqrt{13}+1$.
Solution. Factoring the right-hand side and multiplying both sides by $2 \sqrt{2}$, we get $(x+10) \sqrt{x^{3}-64 x+200}=2 \sqrt{2}(x-4)(x+10)$. From here, there are two possibilities: either $x+10=0$ (then $x=-10$, which does not fit the domain of definition, as the expression under the squa... | 6,\sqrt{13}+1 | Algebra | math-word-problem | olympiads | 0e5aaf6e-3a97-58cf-9eea-3abc2af98101 | [
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"content": "3. [4 points] Solve the equation $\\left(\\frac{x}{2 \\sqrt{2}}+\\frac{5 \\sqrt{2}}{2}\\right) \\sqrt{x^{3}-64 x+200}=x^{2}+6 x-40$.",
"role": "user"
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"content": "<think>\nOkay, so I need to solve this equation: \n\n\\[\n\\left(\\frac{x}{2 \\sqrt{2}}+\\frac{5 \\sqrt{2}}{2}\\right) ... | 0 | 0 | <think>
Okay, so I need to solve this equation:
\[
\left(\frac{x}{2 \sqrt{2}}+\frac{5 \sqrt{2}}{2}\right) \sqrt{x^{3}-64 x+200} = x^{2}+6 x-40
\]
Hmm, that looks a bit intimidating with the square root and the cubic inside it. Let me take it step by step.
First, maybe I should check if there are any obvious solutio... | [
{
"content": "You are a reasoning assistant. Given a chain-of-thought reasoning trace, output a JSON object with a single key 'steps' whose value is an array of step objects. Each step object must include the following keys: 'subgoal' (the intended subgoal for that step). 'content' (the exact text of the reason... | [
{
"contains_final_answer": false,
"content": "Okay, so I need to solve this equation: \n\\[\\left(\\frac{x}{2 \\sqrt{2}}+\\frac{5 \\sqrt{2}}{2}\\right) \\sqrt{x^{3}-64 x+200} = x^{2}+6 x-40\\] \nHmm, that looks a bit intimidating with the square root and the cubic inside it. Let me take it step by step.",
... | 3,106 | 3,162 | 56 |
open-r1/OpenR1-Math-220k | "4. Given that $a$ and $b$ are positive numbers, $a+b=3$. For what values of $a$ and $b$ is $\\sqrt{(...TRUNCATED) | ["<think>\nOkay, so I need to minimize the expression √(a² + 4) + √(b² + 25) given that a and (...TRUNCATED) | "( Hint: Refer to Example 5. Answer: The minimum value is $\\sqrt{58}$, $\\left.a==\\frac{6}{7}, b=\(...TRUNCATED) | \sqrt{58} | Algebra | math-word-problem | cn_contest | 7196d0ba-664d-5dcf-a713-f69fd7f66c66 | [
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open-r1/OpenR1-Math-220k | "5. [5 points] Given the numbers $\\log _{\\sqrt{2 x-8}}(x-4), \\log _{(x-4)^{2}}(5 x-26), \\log _{\(...TRUNCATED) | ["<think>\nOkay, let's see. I need to find the value of x where two of these three logarithms are eq(...TRUNCATED) | "Answer: $x=6$.\n\nSolution. From the condition, it follows that the functions $x-4, 5x-26$ are posi(...TRUNCATED) | 6 | Algebra | math-word-problem | olympiads | eeab361e-c39b-590e-85ec-24f433f8a0d6 | [
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open-r1/OpenR1-Math-220k | "$6 \\cdot 66$ Find all ordered pairs of positive integers $(m, n)$ such that $\\frac{n^{3}+1}{m n-1(...TRUNCATED) | ["<think>\nOkay, so I need to find all ordered pairs of positive integers (m, n) such that (n³ + 1)(...TRUNCATED) | "[Solution] Since $\\left(m n-1, m^{3}\\right)=1$, then $m n-1 \\mid n^{3}+1$ is equivalent to $m n-(...TRUNCATED) | (2,2),(2,1),(3,1),(5,2),(5,3),(1,2),(1,3),(2,5),(3,5) | Number Theory | math-word-problem | olympiads | c8c59f0c-b1e0-5926-b948-624844066304 | [
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open-r1/OpenR1-Math-220k | "Let $k$ be the product of every third positive integer from $2$ to $2006$, that is $k = 2\\cdot 5\\(...TRUNCATED) | ["<think>\nOkay, let's see. The problem is asking for the number of trailing zeros in the product k,(...TRUNCATED) | "To determine the number of zeros at the right end of the decimal representation of \\( k \\), we ne(...TRUNCATED) | 168 | Number Theory | math-word-problem | aops_forum | 2744f8c5-1994-5427-b5aa-c6a984286377 | [
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open-r1/OpenR1-Math-220k | "Four. (20 points) As shown in Figure 3, given that $A$ and $B$ are the endpoints of the major axis (...TRUNCATED) | ["<think>\nOkay, let's try to figure out this problem step by step. So, we have an ellipse with the (...TRUNCATED) | "From the problem, we know that points $A, P, B, M$ lie on the circle $\\odot N$, where the center $(...TRUNCATED) | \frac{x^{2}}{^{2}}+\frac{y^{2}}{(\frac{^{2}}{b})^{2}}=1(|x|<) | Geometry | math-word-problem | olympiads | 381cabf4-d5b4-5259-acdf-e961886633eb | [
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open-r1/OpenR1-Math-220k | "34. Let's determine the amount of calcium carbonate substance. According to the chemical reaction e(...TRUNCATED) | ["<think>\nOkay, so I need to figure out the volume of gas released in this chemical reaction. Let m(...TRUNCATED) | "Answer: 42.37 g\n\n## TOTAL 10 points\n\n## TASK № 2\n\nTo a solution of copper(II) sulfite, an e(...TRUNCATED) | 42.37 | Other | math-word-problem | olympiads | b8c7e178-b2c1-58ec-b423-b4d0eec02734 | [
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open-r1/OpenR1-Math-220k | "## Task B-1.5.\n\nDuring the French Revolution, there was an idea to divide the day (a period of 24(...TRUNCATED) | ["<think>\nOkay, let's see. So the problem is about comparing how fast Marko and Petra solved a prob(...TRUNCATED) | "## Solution.\n\nSince 10 \"decimal hours\" correspond to 24 \"regular hours\", we conclude that 1 \(...TRUNCATED) | 1.8 | Algebra | math-word-problem | olympiads | 77fcf335-45d7-500d-ab15-b63e2f83ae96 | [
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open-r1/OpenR1-Math-220k | "Colin has $900$ Choco Pies. He realizes that for some integer values of $n \\le 900$, if he eats n (...TRUNCATED) | ["<think>\nOkay, let's see. Colin has 900 Choco Pies, and he wants to know how many integer values o(...TRUNCATED) | "To determine how many possible values of \\( n \\) there are such that Colin can eat \\( n \\) pies(...TRUNCATED) | 27 | Number Theory | math-word-problem | aops_forum | e87afcda-7cad-5315-9211-97f0b5564981 | [
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open-r1/OpenR1-Math-220k | 11. Given $a+b+c=0, a^{2}+b^{2}+c^{2}=4$. Then, the value of $a^{4}+b^{4}+c^{4}$ is $\qquad$ . | ["<think>\nAlright, so I have this problem here: given that a + b + c equals zero, and a squared plu(...TRUNCATED) | "11.8.\n\nFrom the known equations, we get $a+b=-c, a^{2}+b^{2}=4-c^{2}$.\n$$\n\\begin{array}{l}\n\\(...TRUNCATED) | 8 | Algebra | math-word-problem | cn_contest | c30c8620-0598-5a96-9218-df329fc77ecc | [
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