已知：a=-2011,b=2010,c=-2009,求a²+b²+c²+ab+bc-ac

分析：先求2(a²+b²+c²+ab+bc-ac),然后配方
2(a²+b²+c²+ab+bc-ac)=2a²+2b²+2c²+2ab+2bc-2ac
=(a²+2ab+b²)+(a²-2ac+c²)+(b²+2bc+c²)
=(a+b)²+(a-b)²+(b+c)²
=(-2011+2010)²+(-2011+2009)²+(2010-2009)²
=1+(-2)²+1=4
故a²+b²+c²+ab+bc-ac=4/2=2错了，答案给的是3啊我的时候加错了，你再看看~ 2(a²+b²+c²+ab+bc-ac)=2a²+2b²+2c²+2ab+2bc-2ac =(a²+2ab+b²)+(a²-2ac+c²)+(b²+2bc+c²) =(a+b)²+(a-b)²+(b+c)² =(-2011+2010)²+(-2011+2009)²+(2010-2009)² =1+(-2)²+1=6故a²+b²+c²+ab+bc-ac=6/2=3