Question

用配方法解下列方程





Answer 1

1、x²-10x+16=0
x²-10x+25=25-16
(x-5)²=9
x=5±3
x1=2,x2=8

2、x²-6x+5=0
x²-6x+9=9-5
(x-3)²=4
x=3±2
x1=1,x2=5

3、3x²-1=4x
3x²-4x=1
3(x²-4/3x+4/9)=1+4/3
(x-2/3)²=7/9

x=2/3±√7/3

4、2x²-30=-√2x
x²+√2/2x-15=0
(x²+√2/2x+1/8)=15+1/8
(x+√2/4)²=121/8

x=-√2/4±11√2/4
x1=-3√2,x2=5√2/2

Answer 2

（1）（x-5)^2-9=0
(x-5+3)(x-5-3)=0
x=2,x=8
(2)(x-3)^2-4=0
(x-3-2)(x-3+2)=0
x=5,x=1
(3)x^2-1/3=4x/3
[x-(2/3)^(1/2)]^2-1=0
[x-(2/3)^(1/2)-1][x-(2/3)^(1/2)+1]=0
x=(2/3)^(1/2)+1
x=(2/3)^(1/2)-1
(4)x^2-15=-(√2)x/2
[x-(√2)/4]^2-121/8=0

[x-(√2)/4-11/2(√2)][x-(√2)/4+11/2(√2)]=0

x=3√2, x=-(5/2)√2

Answer 3

解：2x*2+√2x-30=0
x*2+√2/2x-15=0
x*2+√2/2x+(√2/4)*2=15+(√2/4)*2
(x+√2/4)*2=242/16
x=±11√2/4-√2/4
x1=5√2/2
x2=-3√2