2022-08-12 06:30:19 +00:00
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# 均贫富
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2022-08-16 05:56:50 +00:00
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姐姐：🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎 16个
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2022-08-16 05:58:31 +00:00
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弟弟：🍎🍎🍎🍎🍎🍎🍎🍎🍎🍎 10个
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2022-08-16 05:56:50 +00:00
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问题：姐姐给弟弟几个苹果后两个人的苹果就一样多了？
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2022-08-12 06:30:19 +00:00
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## 解法1
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2022-08-16 05:46:33 +00:00
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$
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\begin{aligned}
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2022-08-16 10:11:33 +00:00
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a - x &= b + x &({a}\in\Bbb{N},{b}\in\Bbb{N},a>b) \\\\
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2022-08-18 10:15:37 +00:00
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a - x + x &= b + 2x &(等式两侧同加x) \\\\
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a &= b + 2x \\\\
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a - b &= b -b+ 2x &(等式两侧同减b) \\\\
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a -b &= 2x \\\\
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2x &= a - b &(交换等式两侧) \\\\
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2022-08-16 05:48:00 +00:00
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x &= \dfrac{a-b}{2} &(等式两侧同除以2)
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2022-08-16 05:46:33 +00:00
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\end{aligned}
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$
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2022-08-12 06:30:19 +00:00
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## 解法2
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2022-08-16 05:47:38 +00:00
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$ x = \dfrac{a+b}{2} - b $
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2022-08-18 10:15:37 +00:00
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## 其实两个解法的结果是一样的
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$\dfrac{a+b}{2} - b= \dfrac{a+b}{2}-\dfrac{2b}{2} = \dfrac{a+b-2b}{2} = \dfrac{a-b}{2}$
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