Question

用配方法解下列方程 怎么解？ (1) 2x²+3=5x (2) -3x²-2x+1=0

Answer 1

你好！

2x² - 5x = - 3
x² - 5/2 x = - 3/2
x² - 5/2 x + 25/16 = - 3/2 + 25/16
(x - 5/4)² = 1/16
x - 5/4 = ± 1/4
x₁ = 3/2 ，x₂ = 1

-3x² - 2x +1 = 0
3x² + 2x = 1
x² + 2/3 x = 1/3
x² + 2/3 x + 1/9 = 1/3 + 1/9
(x+1/3)² = 4/9
x+ 1/3 = ± 2/3
x₁ = 1/3 ，x₂ = - 1

Answer 2

2x² - 5x+3 =0
x² - 5/2 x+ 3/2 =0
x² - 5/2 x + 25/16+3/2 - 25/16 =0
(x - 5/4)² = 1/16
x - 5/4 = ± 1/4
x₁ = 3/2 ，x₂ = 1

-3x² - 2x +1 = 0
3x² + 2x-1 = 0
x² + 2/3 x- 1/3= 0
x² + 2/3 x + 1/9 -1/3 - 1/9 =0
(x+1/3)² = 4/9
x+ 1/3 = ± 2/3
x₁ = 1/3 ，x₂ = - 1