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
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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,则ab](/uploads/image/z/643771-19-1.jpg?t=%E9%98%85%E8%AF%BB%E7%90%86%E8%A7%A3%E9%A2%98%EF%BC%9A%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%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%2C%E5%88%99ab)
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
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,则ab
(2011-x)²=(x-2011)²
设(2013-x)=a,(x-2011)=b,
a+b=2013-x+x-2011=2
a^2+b^2=4028
(a+b)^2-2ab=2048
2^2-2ab=2048
-2ab=2044
-ab=1022
-(2013-x)(x-2011)=1022
(2013-x)(2011-x)=-1022
设(2013-x)=a,(x-2011)=b,
则a²+b²=4028,且a+b=(2013-x)+(x-2011)=2,
∵(a+b)²=a²+2ab+b²
∴ab=[(a+b)²-(a²+b²)]/2=(2²-4028)/2=-2012
即(2013-x)(2011-x)的值为-2012.