用配方法解方程:(1)x눀-1=-x(2)2x눀-6x+2=0

2024-12-21 15:15:01
推荐回答(2个)
回答1:

(1)x²-1=-x
x²﹣x﹣1=0
x²﹣2×﹙1/2﹚x﹢1/4﹣1/4﹣1=0
﹙x﹣1/2﹚²=﹙√5/2﹚²
x﹣1/2=±√5/2
∴x=﹙1±√5﹚/2
(2)2x²-6x+2=0
x²-x+1=0
﹙x﹣1/2﹚²=﹣3/4
﹙x﹣1/2﹚²≧0
∴无实数根

回答2:

x²-1=-x
x²+x-1=0
(x+1/2)²-1/4-1=0
(x+1/2)²=5/4
x+1/2=±√5/2
x=-1/2±√5/2

(2)2x²-6x+2=0
x²-3x+1=0

(x-3/2)²-9/4+1=0
(x-3/2)²=5/4
x-3/2=±√5/2

x=3/2±√5/2