若x满足(210-x)(x-200)=-204,求(2013-x)(2011-x) 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
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![若x满足(210-x)(x-200)=-204,求(2013-x)(2011-x) 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](/uploads/image/z/1084776-24-6.jpg?t=%E8%8B%A5x%E6%BB%A1%E8%B6%B3%28210-x%29%28x-200%29%3D-204%2C%E6%B1%82%282013-x%29%282011-x%29+%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%892%2B%EF%BC%88x-200%EF%BC%892%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%3D-204%2C%E4%B8%94a%2Bb%3D%EF%BC%88210-x%EF%BC%89%2B%EF%BC%88x-200%EF%BC%89%3D10%2C%E2%88%B5%EF%BC%88a%2Bb%EF%BC%892%3Da2%2B2ab%2Bb2)
若x满足(210-x)(x-200)=-204,求(2013-x)(2011-x) 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
若x满足(210-x)(x-200)=-204,求(2013-x)(2011-x)
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”.
若x满足(210-x)(x-200)=-204,求(2013-x)(2011-x) 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
解由(2013-x)2+(2011-x)2=4028
设a=2013-x,b=x-2011
即a²+b²=4028
a+b=(2013-x)+(x-2011)=2
即a²+2ab+b²=(a+b)²=2²=4
即a²+2ab+b²=4
即2ab+a²+b²=4
即2ab+4028=4
即2ab=4024
即ab=2012
即(2013-x)(2011-x)
=-(2013-x)(x-2011)
=-ab
=-2012
设2013-x=a,2011-x=b则a²+b²=4028,a-b=2,又因为(a-b)²=a²-2ab+b²所以ab=(a-b)²-(a²+b²)=4-4028=-4024即答案是4024
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