| 模型 | 模型答案 | 正确答案 |
|---|---|---|
| 金声玉亮2.0 | B. 13 |
C |
| deepseekr1 | To solve for \(4x^2 + 9y^2\), start by expanding \((2x + 3y)^2\): \[ (2x + 3y)^2 = (2x)^2 + 2(2x)(3y) + (3y)^2 = 4x^2 + 12xy + 9y^2 \] Given \((2x + 3y)^2 = 4\), substitute the expansion: \[ 4x^2 + 12xy + 9y^2 = 4 \] We need \(4x^2 + 9y^2\). Subtract \(12xy\) from both sides: \[ 4x^2 + 9y^2 = 4 - 12xy \] Substitute \(xy = -5\): \[ 4x^2 + 9y^2 = 4 - 12(-5) = 4 + 60 = 64 \] Thus, the value of \(4x^2 + 9y^2\) is **64**, corresponding to option **C**. **Answer:** C |
C |
| gpto1 | C | C |
| GPT-4o | To find the value of \(4x^2 + 9y^2\), we start by expanding and simplifying the given equation \((2x + 3y)^2 = 4\). First, expand \((2x + 3y)^2\): \[ (2x + 3y)^2 = 4x^2 + 12xy + 9y^2 \] Given that \((2x + 3y)^2 = 4\), we can equate: \[ 4x^2 + 12xy + 9y^2 = 4 \] We are also given \(xy = -5\). Substitute \(xy = -5\) into the equation: \[ 4x^2 + 12(-5) + 9y^2 = 4 \] Simplify the equation: \[ 4x^2 - 60 + 9y^2 = 4 \] Add 60 to both sides of the equation: \[ 4x^2 + 9y^2 = 64 \] Thus, the value of \(4x^2 + 9y^2\) is: \[ \boxed{64} \] So the correct answer is: C. 64 |
C |
| llama3.1-70B-Instruct | B |
C |
| llama3.1-405B-Instruct | We have that \begin{align*} (2x + 3y)^2 &= 4\\ \Rightarrow\qquad 4x^2 + 12xy + 9y^2 &= 4\\ \Rightarrow\qquad 4x^2 + 12(-5) + 9y^2 &= 4\\ \Rightarrow\qquad 4x^2 + 9y^2 &= 4 + 60 = \boxed{64}. \end{align*} The best answer is C. |
C |
| DeepSeek-Coder-V2 | To solve the problem, we start with the given equations: 1. \((2x + 3y)^2 = 4\) 2. \(xy = -5\) First, expand the square in the first equation: \[ (2x + 3y)^2 = 4 \implies 4x^2 + 12xy + 9y^2 = 4 \] We know from the second equation that \(xy = -5\). Substitute \(xy = -5\) into the expanded equation: \[ 4x^2 + 12(-5) + 9y^2 = 4 \] Simplify the equation: \[ 4x^2 - 60 + 9y^2 = 4 \] Add 60 to both sides to isolate the terms involving \(x\) and \(y\): \[ 4x^2 + 9y^2 = 4 + 60 \] \[ 4x^2 + 9y^2 = 64 \] Thus, the value of \(4x^2 + 9y^2\) is: \[ \boxed{C} \] |
C |
| Qwen2-72B-Instruct | C. 64 | C |
| baichuan4 | B | C |
| doubao | We know that $(2x + 3y)^2 = 4x^2 + 12xy + 9y^2 = 4$. And $xy = -5$. So $12xy = 12\times(-5) = -60$. Then $4x^2 + 9y^2 = (2x + 3y)^2 - 12xy = 4 - (-60) = 64$. So the answer is C. | C |
| minimax | To find the value of $4x^2 + 9y^2$, we can expand the given equation $(2x + 3y)^2 = 4$ and then manipulate it to get the desired expression. Expanding $(2x + 3y)^2$ gives us: $(2x + 3y)^2 = 4x^2 + 12xy + 9y^2$ We know that this equals 4, so: $4x^2 + 12xy + 9y^2 = 4$ We are also given that $xy = -5$. We can use this to replace $12xy$ in the equation: $4x^2 + 12(-5) + 9y^2 = 4$ Now, simplify the middle term: $4x^2 - 60 + 9y^2 = 4$ We want to find $4x^2 + 9y^2$, so we add $60$ to both sides to isolate the terms we want: $4x^2 + 9y^2 = 4 + 60$ $4x^2 + 9y^2 = 64$ Therefore, the value of $4x^2 + 9y^2$ is 64. The correct answer is: C. 64 |
C |
| kimi | To solve this problem, we can use the given equations to find the value of \(4x^2 + 9y^2\). First, let's expand the given equation \((2x + 3y)^2 = 4\): \[ (2x + 3y)^2 = 4x^2 + 12xy + 9y^2 = 4 \] We are also given that \(xy = -5\). We can substitute this into the expanded equation: \[ 4x^2 + 12(-5) + 9y^2 = 4 \] \[ 4x^2 - 60 + 9y^2 = 4 \] Now, we want to find the value of \(4x^2 + 9y^2\). Let's isolate this term by adding 60 to both sides of the equation: \[ 4x^2 + 9y^2 = 4 + 60 \] \[ 4x^2 + 9y^2 = 64 \] So the value of \(4x^2 + 9y^2\) is 64. Answer: C. 64 |
C |
| wenxinyiyan | C Explanation: Given $(2x + 3y)^2 = 4$ and $xy = -5$, we can expand the square to get: $(2x + 3y)^2 = 4x^2 + 12xy + 9y^2 = 4$ Then, we can rearrange this equation to solve for $4x^2 + 9y^2$: $4x^2 + 9y^2 = 4 - 12xy$ Using the given value of $xy = -5$, we can substitute this into the equation: $4x^2 + 9y^2 = 4 - 12(-5) = 4 + 60 = 64$ So, the value of $4x^2 + 9y^2$ is 64. |
C |
| zhipu | To solve the given problem, let's start by expanding the expression \((2x + 3y)^2\): \[ (2x + 3y)^2 = 4x^2 + 12xy + 9y^2 \] We are given that \((2x + 3y)^2 = 4\). Therefore, \[ 4x^2 + 12xy + 9y^2 = 4 \] We are also given that \(xy = -5\). Substituting \(xy = -5\) into the equation, we get: \[ 4x^2 + 12(-5) + 9y^2 = 4 \] Simplify the equation: \[ 4x^2 - 60 + 9y^2 = 4 \] Add 60 to both sides to isolate the terms involving \(x^2\) and \(y^2\): \[ 4x^2 + 9y^2 = 64 \] Thus, the value of \(4x^2 + 9y^2\) is 64. The correct answer is: C. 64 |
C |
| gpto1 | C | C |
| deepseekv3 | We are given the following equations: 1. \((2x + 3y)^2 = 4\) 2. \(xy = -5\) We need to find the value of \(4x^2 + 9y^2\). First, expand \((2x + 3y)^2\): \[ (2x + 3y)^2 = 4x^2 + 12xy + 9y^2 \] We know that \((2x + 3y)^2 = 4\), so: \[ 4x^2 + 12xy + 9y^2 = 4 \] We are also given that \(xy = -5\). Substitute this into the equation: \[ 4x^2 + 12(-5) + 9y^2 = 4 \] Simplify the equation: \[ 4x^2 - 60 + 9y^2 = 4 \] Add 60 to both sides: \[ 4x^2 + 9y^2 = 64 \] Therefore, the value of \(4x^2 + 9y^2\) is \(64\). The correct answer is \(\boxed{C}\). |
C |