因式分解 (31 10:1:52)
问题描述：
因式分解 (31 10:1:52)
1.a^2-b^2-c^2+2bc 2.x^2-y^2-x+1/4
3.已知x,y互为相反数,且(x+2)^2-(y+2)^2=4,求x,y的值
答
1.a^2-b^2-c^2+2bc
=a^2-(b^2+c^2-2bc)
=a^2-(b-c)^2
=(a+b-c)(a-b+c)
2.x^2-y^2-x+1/4
=(x^2-x+1/4)-y^2
=(x-1/2)^2-y^2
=(x-1/2+y)(x-1/2-y)
3.由（x+2)^2-(y+2)^2=4得
（x+2+y+2)(x+2-y-2)=4
即（x+y+4)(x-y)=4
x,y互为相反数,则x+y=0 x-y=2x代入（x+y+4)(x-y)=4得
x=1/2 y=-1/2