Question

帮忙解答几道题.全用配方法解.

(1)x^2-6x=5
(2)4x^2-4x-1=0
(3)x^2-x+1=0
(4)2x^2-3x-2=0

Answer 1

(1)x^2-6x=5
x^2-6x+9=5+9
(x-3)²=14
x=正负根号14 + 3
(2)4x^2-4x-1=0
4（x²-x+0.25）=1+1
4（x-0.5）²=2
（x-0.5）²=0.5
x=正负根号0.5 +0.5
=（正负根号2 + 1）/2
(3)x^2-x+1=0
x²-x+0.25=-0.75
（x-0.5）²=-0.75
无解
(4)2x^2-3x-2=0
2（x²-1.5x）=2
x²-1.5x=1
x²-1.5x+0.75²=1+0.75²
（x-0.75）²=25/16
x=正负5/4 +0.75
x=2或者x=-0.5