初二上学期数学实数范围内分解因式

题目

初二上学期数学实数范围内分解因式
在实数范围内分解因式
1.x²+x-1
2.x²-2x-6
3.2x²+8x-7
4.x²-5xy+3y²
5.-2x²-3x+6
6.4x²y²+xy-1

答案

1.x²+x-1
=x²+x+1/4-3/4
=(x+1/2)²-3/4
=(x+1/2+√3/2)(x+1/2-√3/2)
2.x²-2x-6
=(x²-2x+1)-7
=(x-1)²-7
=(x-1+√7)(x-1-√7)
3.2x²+8x-7
=2(x²+4x+4-15/2)
=2(x+2-√30/2)(x+2+√30/2)
4.x²-5xy+3y²
=(x²-5xy+25y²/4-13y²/4)
=(x-5y/2+√13y/2)(x-5y/2-√13y/2)
5.-2x²-3x+6
=-2(x²+3x+9/4-21/4)
=-2(x+3/2+√21/2)(x+3/2-√21/2)
6.4x²y²+xy-1
=4x²y²+xy+1/4-5/4
=(2xy+1/2+√5/2)(2xy+1/2-√5/2)