阅读理解题:若x满足(210-x)(x-200)=-204,试求(210-x)²+(x-200)²的
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”.