difficulty int64 | source stringclasses 1
value | domain stringclasses 1
value | conversations listlengths 2 2 |
|---|---|---|---|
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "Find the product of the roots of the equation \\[x^2 \\sqrt{x} - 3x^2 + 2\\sqrt{x} + 5 = 0,\\]given that all of the roots are real and nonnegative."
},
{
"from": "qwen3",
"value": "<think>\nOkay, so I need to find the product of the roots of this equation: $x^2 \\sqr... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "Compute the product of the roots of the equation \\[x\\sqrt{x} - 3x + 2\\sqrt{x} + 4 = 0,\\]given that all of the roots are real and nonnegative."
},
{
"from": "qwen3",
"value": "<think>\nOkay, so I need to find the product of the roots of this equation: $x\\sqrt{x} ... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "In a choir, there are 6 sopranos and 6 altos. In how many ways can they stand in a circle around the conductor if each singer stands next to two singers of the opposite vocal type? (Two arrangements are the same if one is a rotation of the other.)"
},
{
"from": "qwen3",
... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "Let $a$ and $b$ be integers, and let $f$ be a function taking the integers to the integers such that\n\n$$f(a)f(b) + f(a+b) = f(ab) + f(a) + f(b)$$\n\nfor all $a$ and $b$. For how many values of $k$ does there exist such a function $f$ such that $f(f(0)) = k$?"
},
{
"fr... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "Let m be a positive integer. Determine the largest possible value of $m$ such that $m(m^2-n^2)+n$ is divisible by 8 for all positive integers n less than m."
},
{
"from": "qwen3",
"value": "<think>\nOkay, so I need to figure out the largest possible value of m such t... |
null | ai2-adapt-dev/openmath-2-math | math | [
{
"from": "human",
"value": "In a right-angled triangle $ABC$, the altitude from the right angle $C$ meets the hypotenuse $AB$ at point $D$. A square $EFMN$ is inscribed in the triangle such that its vertices $E$ and $F$ lie on the hypotenuse $AB$, and its vertices $M$ and $N$ lie on the legs of the triangl... |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"The function $g(x),$ defined for $0 \\le x \\le 1,$ has the following prop(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"Factor completely over the set of polynomials with rational coefficients:\(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"A triangle $\\triangle ABC$ has vertices $A(0, 0)$, $B(8, 0)$, and $C(4, 4(...TRUNCATED) |
null | ai2-adapt-dev/openmath-2-math | math | [{"from":"human","value":"In a department store there were \\(n\\) light bulbs of the same type. Eve(...TRUNCATED) |
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