阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”设(210-x)=a,(x-200)=b
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![阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”设(210-x)=a,(x-200)=b](/uploads/image/z/369015-15-5.jpg?t=%E9%98%85%E8%AF%BB%E7%90%86%E8%A7%A3%E9%A2%98%EF%BC%9A%E2%80%9C%E8%8B%A5x%E6%BB%A1%E8%B6%B3%EF%BC%88210-x%EF%BC%89%EF%BC%88x-200%EF%BC%89%3D-204%2C%E8%AF%95%E6%B1%82%EF%BC%88210-x%EF%BC%89%26%23178%3B%2B%EF%BC%88x-200%EF%BC%89%26%23178%3B%E7%9A%84%E5%80%BC%2C%E2%80%9D%E9%98%85%E8%AF%BB%E7%90%86%E8%A7%A3%E9%A2%98%EF%BC%9A%E2%80%9C%E8%8B%A5x%E6%BB%A1%E8%B6%B3%EF%BC%88210-x%EF%BC%89%EF%BC%88x-200%EF%BC%89%3D-204%2C%E8%AF%95%E6%B1%82%EF%BC%88210-x%EF%BC%89%26%23178%3B%2B%EF%BC%88x-200%EF%BC%89%26%23178%3B%E7%9A%84%E5%80%BC%2C%E2%80%9D%E8%AE%BE%EF%BC%88210-x%EF%BC%89%3Da%2C%EF%BC%88x-200%EF%BC%89%3Db)
阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”设(210-x)=a,(x-200)=b
阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”
阅读理解题:
“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”
设(210-x)=a,(x-200)=b,
则ab=-204,且a+b=(210-x)+(x-200)=10,
∵(a+b)²=a²+2ab+b²
∴a²+b²=(a+b)²-2ab=10²-2(-204)=508
即(210-x)²+(x-200)²的值为508.
同学们,根据材料,请你完成下面这一题的解答过程:
“若x满足(2013-x)²+(2011-x)²=4028,试求(2013-x)(2011-x)的值”.
阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”阅读理解题:“若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的值,”设(210-x)=a,(x-200)=b
上面的示例提供的是下面题目的解题思路,只要按照他的解法照葫芦画瓢就可以了,只不过是个逆向过程,应该是不难的:
设(2013-x)=a,(2011-x)=b,则a²+b²=4028
且a-b=2(这个等量关系是根据a,b看出来的,题目中(210-x)=a,(x-200)=b,ab相加能把x消掉,得到ab的常数关系,这个也是一样的(2013-x)=a,(2011-x)=b,a-b能把x消掉);
∵(a-b)²=a²-2ab+b²
∴2ab=a²+b²-(a-b)²=4028-2²=4024
则ab=2012
即(2013-x)(2011-x)的值为2012.
所以仔细分析下,其实不难的,遇到这样的题要试着找找关系,祝好.