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[{"content":"Find the product of the real roots of $x^4 - 2x^2 - 2x + 1 = 0.$","role":"user"},{"cont(...TRUNCATED) | Find the product of the real roots of $x^4 - 2x^2 - 2x + 1 = 0.$ | Find the product of the real roots of $x^4 - 2x^2 - 2x + 1 = 0.$ | ai2-adapt-dev/openmath-2-math | "Given the polynomial:\n\\[\nx^4 - 2x^2 - 2x + 1 = 0,\n\\]\nwe want to find the product of its real (...TRUNCATED) | 2,423 | 15,950 | 155 | ["Alright, so I need to find the product of the real roots of the equation \\(x^4 - 2x^2 - 2x + 1 = (...TRUNCATED) | ["To find the product of the real roots of the equation \\(x^4 - 2x^2 - 2x + 1 = 0\\), we start by n(...TRUNCATED) | ["<think>\nAlright, so I need to find the product of the real roots of the equation \\(x^4 - 2x^2 - (...TRUNCATED) | [
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[{"content":"The surface area of a certain rectangular solid is $384\\text{ cm}^2$, its volume is $1(...TRUNCATED) | "The surface area of a certain rectangular solid is $384\\text{ cm}^2$, its volume is $128\\text{ cm(...TRUNCATED) | "The surface area of a certain rectangular solid is $384\\text{ cm}^2$, its volume is $128\\text{ cm(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Let the dimensions of the rectangular solid be \\(a-d\\), \\(a\\), and \\(a+d\\), where \\(a\\), \\(...TRUNCATED) | 10,042 | 17,262 | 2,867 | ["Alright, so I have this problem about a rectangular solid. The surface area is 384 cm², the volum(...TRUNCATED) | ["Given a rectangular solid with a surface area of \\(384 \\, \\text{cm}^2\\), a volume of \\(128 \\(...TRUNCATED) | ["<think>\nAlright, so I have this problem about a rectangular solid. The surface area is 384 cm², (...TRUNCATED) | [
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] | "The response consists of multiple long paragraphs that exceed 750 words. Although it is extensively(...TRUNCATED) | ["<think>\nAlright, so I have this problem about a rectangular solid. The surface area is 384 cm², (...TRUNCATED) | "<think>\nOkay, let me try to figure this problem out. So we have a rectangular solid with surface a(...TRUNCATED) | [{"from":"human","value":"The surface area of a certain rectangular solid is $384\\text{ cm}^2$, its(...TRUNCATED) |
[{"content":"Find a cubic polynomial, in $x,$ with integer coefficients such that the polynomial has(...TRUNCATED) | "Find a cubic polynomial, in $x,$ with integer coefficients such that the polynomial has only one re(...TRUNCATED) | "Find a cubic polynomial, in $x,$ with integer coefficients such that the polynomial has only one re(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "We want a cubic polynomial \\( p(x) \\) with integer coefficients such that:\n\n1. \\( p(x) \\) has(...TRUNCATED) | 30,123 | 14,117 | 3,712 | ["Okay, so I need to find a cubic polynomial with integer coefficients. The requirements are that it(...TRUNCATED) | ["Given the problem of finding a cubic polynomial with integer coefficients that has only one real r(...TRUNCATED) | ["<think>\nOkay, so I need to find a cubic polynomial with integer coefficients. The requirements ar(...TRUNCATED) | [
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] | The answer does not contain any long paragraphs that exceed 750 words. | ["<think>\nOkay, so I need to find a cubic polynomial with integer coefficients. The requirements ar(...TRUNCATED) | "<think>\nOkay, let me try to figure out how to find this cubic polynomial. The problem says it need(...TRUNCATED) | [{"from":"human","value":"Find a cubic polynomial, in $x,$ with integer coefficients such that the p(...TRUNCATED) |
[{"content":"Find the number of distinct quadrilaterals that can be formed by connecting four differ(...TRUNCATED) | "Find the number of distinct quadrilaterals that can be formed by connecting four different vertices(...TRUNCATED) | "Find the number of distinct quadrilaterals that can be formed by connecting four different vertices(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "First, let's understand the problem and the shape:\n\n- A **regular octahedron** has **6 vertices**(...TRUNCATED) | 676 | 10,422 | 42 | ["Okay, so I need to figure out how many distinct quadrilaterals can be formed by connecting four di(...TRUNCATED) | ["To determine the number of distinct quadrilaterals that can be formed by connecting four different(...TRUNCATED) | ["<think>\nOkay, so I need to figure out how many distinct quadrilaterals can be formed by connectin(...TRUNCATED) | [
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] | "The answer does not contain any paragraphs exceeding 750 words; it consists of structured reasoning(...TRUNCATED) | ["<think>\nOkay, so I need to figure out how many distinct quadrilaterals can be formed by connectin(...TRUNCATED) | "<think>\nOkay, so I need to find the number of distinct quadrilaterals that can be formed by connec(...TRUNCATED) | [{"from":"human","value":"Find the number of distinct quadrilaterals that can be formed by connectin(...TRUNCATED) |
[{"content":"In a certain game, a player is presented with a set of $n$ cards, each with a unique co(...TRUNCATED) | "In a certain game, a player is presented with a set of $n$ cards, each with a unique color. The pla(...TRUNCATED) | "In a certain game, a player is presented with a set of $n$ cards, each with a unique color. The pla(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:**\n\nThere are \\( n \\) cards, each of a unique color, labeled \\( 1, 2, \\(...TRUNCATED) | 3,295 | 16,664 | 318 | ["Okay, let's tackle this problem step by step. First, I need to make sure I understand what's being(...TRUNCATED) | ["The problem involves a game with \\( n \\) cards, each of a unique color, where a \"set\" is defin(...TRUNCATED) | ["<think>\nOkay, let's tackle this problem step by step. First, I need to make sure I understand wha(...TRUNCATED) | [
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[{"content":"A committee consisting of 10 members is to be formed from a group of 20 people. What is(...TRUNCATED) | "A committee consisting of 10 members is to be formed from a group of 20 people. What is the probabi(...TRUNCATED) | "A committee consisting of 10 members is to be formed from a group of 20 people. What is the probabi(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:**\n\nWe have a group of 20 people, and from them, we want to choose a commit(...TRUNCATED) | 32,434 | 10,943 | 948 | ["Okay, so I need to find the probability that in a committee of 10 members, none of them share the (...TRUNCATED) | ["To find the probability that no two committee members will have the same birthday when forming a c(...TRUNCATED) | ["<think>\nOkay, so I need to find the probability that in a committee of 10 members, none of them s(...TRUNCATED) | [
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] | "The provided answer contains lengthy sections of text that exceed the threshold of 750 words, makin(...TRUNCATED) | ["<think>\nOkay, so I need to find the probability that in a committee of 10 members, none of them s(...TRUNCATED) | "<think>\nOkay, so I need to find the probability that in a committee of 10 members, none of them sh(...TRUNCATED) | [{"from":"human","value":"A committee consisting of 10 members is to be formed from a group of 20 pe(...TRUNCATED) |
[{"content":"Let $P(x) = x^3 + ax^2 + bx + c$, and $Q(x) = x^2 - 7x + k$. Given that the remainder o(...TRUNCATED) | "Let $P(x) = x^3 + ax^2 + bx + c$, and $Q(x) = x^2 - 7x + k$. Given that the remainder of $\\frac{P((...TRUNCATED) | "Let $P(x) = x^3 + ax^2 + bx + c$, and $Q(x) = x^2 - 7x + k$. Given that the remainder of $\\frac{P((...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n\\[\nP(x) = x^3 + a x^2 + b x + c\n\\]\nand\n\\[\nQ(x) = x^2 - 7x + k.\n\\]\n\nThe division(...TRUNCATED) | 42,283 | 17,533 | 691 | ["Okay, so I need to find the value of ak given that when polynomial P(x) is divided by Q(x), the re(...TRUNCATED) | ["Given the polynomials \\( P(x) = x^3 + ax^2 + bx + c \\) and \\( Q(x) = x^2 - 7x + k \\), we know (...TRUNCATED) | ["<think>\nOkay, so I need to find the value of ak given that when polynomial P(x) is divided by Q(x(...TRUNCATED) | [
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] | "The provided answer does not contain any long paragraphs, as all blocks of text are separated by bl(...TRUNCATED) | ["<think>\nOkay, so I need to find the value of ak given that when polynomial P(x) is divided by Q(x(...TRUNCATED) | "<think>\nAlright, so I need to find the value of \\( ak \\) given that when the polynomial \\( P(x)(...TRUNCATED) | [{"from":"human","value":"Let $P(x) = x^3 + ax^2 + bx + c$, and $Q(x) = x^2 - 7x + k$. Given that th(...TRUNCATED) |
[{"content":"A square 10cm on each side has four quarter circles drawn with centers at the four corn(...TRUNCATED) | "A square 10cm on each side has four quarter circles drawn with centers at the four corners. How man(...TRUNCATED) | "A square 10cm on each side has four quarter circles drawn with centers at the four corners. How man(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "**Problem restatement:**\n\nA square has side length 10 cm. At each of its four corners, a quarter (...TRUNCATED) | 31,025 | 22,580 | 533 | ["Okay, so I need to find the area of the shaded region in this square with four quarter circles. Le(...TRUNCATED) | ["To find the area of the shaded region in the square with four quarter circles, we start by noting (...TRUNCATED) | ["<think>\nOkay, so I need to find the area of the shaded region in this square with four quarter ci(...TRUNCATED) | [
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[{"content":"Let $\\mathbf{p}$ be a vector in a 2D space. Let $\\mathbf{q}$ and $\\mathbf{r}$ be vec(...TRUNCATED) | "Let $\\mathbf{p}$ be a vector in a 2D space. Let $\\mathbf{q}$ and $\\mathbf{r}$ be vectors, and le(...TRUNCATED) | "Let $\\mathbf{p}$ be a vector in a 2D space. Let $\\mathbf{q}$ and $\\mathbf{r}$ be vectors, and le(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given:\n\n- \\(\\mathbf{p} = \\begin{pmatrix} -5 \\\\ 1 \\end{pmatrix}\\)\n- \\(\\mathbf{q} = \\beg(...TRUNCATED) | 42,625 | 20,337 | 1,255 | ["Okay, so I need to find the square of the norm of vector r, given that vector q is the reflection (...TRUNCATED) | ["Given vectors \\(\\mathbf{p} = \\begin{pmatrix} -5 \\\\ 1 \\end{pmatrix}\\) and \\(\\mathbf{q} = \(...TRUNCATED) | ["<think>\nOkay, so I need to find the square of the norm of vector r, given that vector q is the re(...TRUNCATED) | [
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[{"content":"Solve the following system of equations:\n$$\\left\\{ \\begin{array}{l}\nx^3+y^3+z^3=3x(...TRUNCATED) | "Solve the following system of equations:\n$$\\left\\{ \\begin{array}{l}\nx^3+y^3+z^3=3xyz\\\\\nx+y+(...TRUNCATED) | "Solve the following system of equations:\n$$\\left\\{ \\begin{array}{l}\nx^3+y^3+z^3=3xyz\\\\\nx+y+(...TRUNCATED) | ai2-adapt-dev/openmath-2-math | "Given the system:\n\\[\n\\begin{cases}\nx^3 + y^3 + z^3 = 3xyz \\\\\nx + y + z = 1 \\\\\nx^2 + y^2 (...TRUNCATED) | 33,169 | 10,777 | 1,459 | ["Okay, so I need to solve this system of equations:\n\n$$\n\\begin{cases}\nx^3 + y^3 + z^3 = 3xyz \(...TRUNCATED) | ["Given the system of equations:\n\n$$\n\\begin{cases}\nx^3 + y^3 + z^3 = 3xyz \\\\\nx + y + z = 1 \(...TRUNCATED) | ["<think>\nOkay, so I need to solve this system of equations:\n\n$$\n\\begin{cases}\nx^3 + y^3 + z^3(...TRUNCATED) | [
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] | The provided answer consists of multiple short paragraphs, none of which exceed 750 words. | ["<think>\nOkay, so I need to solve this system of equations:\n\n$$\n\\begin{cases}\nx^3 + y^3 + z^3(...TRUNCATED) | "<think>\nOkay, so I have this system of equations to solve:\n\n1. \\( x^3 + y^3 + z^3 = 3xyz \\)\n2(...TRUNCATED) | [{"from":"human","value":"Solve the following system of equations:\n$$\\left\\{ \\begin{array}{l}\nx(...TRUNCATED) |
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