Question

配方法因式分解：2x²-4x-9

2x²-4x-9
=2x²-4x+2-11
=2(x-1)²-11
=2[(x-1)²-22]
=2(x-1+√22)(x-1-√22)
怎么变成=2(x-1)²-11
=2[(x-1)²-22]
那个22怎么回事啊？

Answer 1

我也发现了，写错了，呵呵。再解一遍吧，不好意思啊。
2x²-4x-9
=2x²-4x+2-11
=2(x-1)²-11
=2[(x-1)²-11/2]
=2(x-1+√22/2)(x-1-√22/2)
不应该是√22，应该是(√22)/2

Answer 2

2x²-4x-9
=2（x^2-2x+1)-9-2
=2(x-1)^2-11
=2[(x-1)^2-5.5]
=2(x-1+√5.5）（x-1-√5.5）平方差公式

Answer 3

错了。

应该是：
2x²-4x-9
=2x²-4x+2-11
=2(x-1)²-11
=2[(x-1)²-（11/2）]
=2{(x-1)²-[（√22）/2]²}
=2[x-1+(√22)/2][(x-1-(√22)/2]