x-4=(x-4)²,因式分解法解方程

Question

x-4=(x-4)²

（5x-1)(2x+4)=3x+6

x²-3x-18=0

2y²-5y+2=0

x²+5=2（根号5）x

(3x+2)²-4x²=0

解关于x的方程2x²-mx=15m

Answer 1

x-4=(x-4)²
(x-4)² - (x-4) = 0
(x-4)(x-4-1) = 0
(x-4)(x-5) = 0
x=4 或 x=5

（5x-1)(2x+4)=3x+6
（5x-1)(2x+4) - (3x+6) = 0
2(5x-1)(x+2) - 3(x+2) = 0
(x+2) { 2(5x-1) - 3} = 0
(x+2)(10x-5) =0
(x+2)(2x-1) = 0
x=-2 或 x=1/2

x²-3x-18=0
(x-6)(x+3) = 0
x=6 或 x=-3

2y²-5y+2=0
(2y-1)(y-2) = 0
y=1/2 或 x=2

x²+5=2（根号5）x
x² - 2√5x + 5 = 0
(x-√5)² = 0
x = √5 重根

(3x+2)²-4x²=0
(3x+2+2x)(3x+2-2x) = 0
(5x+2)(x+2) = 0
x=-2/5 或 x=-2

2x²-mx=15m
2x²-mx-15m = 0
(x-3m)(2x+5m) = 0
x=3m 或 x=-2.5m

Answer 2

1.（X-4)-(x-4)²=0
(x-4)(1-x+4)=0
x=4 x=5
2.10x²+18x-4=3x+6
10x²+15x-10=0
x²+1.5x-1=0
x=-2 x=0.5
3.(x-6)(x+3)=0
x=6 x=-3
4.x²-2（根号5）x+5=0
(x-根号5)²=0
x=根号5
5.(3x+2+2x)(3x+2+-2x)=0
(5x+2)(x+2)=0
x=-2/5 x=-2
6.2x²-mx-15m=0
x²-0.5mx-7.5mx=0
(x-3m)(x+2.5m)=0
x=3m x=-2.5m

Answer 3

(x+y-2xy)(x+y-2)+(1-xy)^2
=(x+y)^2-2(1+xy)(x+y)+4xy+1-2xy+x^2y^2
=(x+y)^2-2(1+xy)(x+y)+(1+xy)^2
=(x+y)^2-(1+xy)(x+y)-(1+xy)(x+y)+(1+xy)^2
=(x+y)(x+y-1-xy)-(1+xy)(x+y-1-xy)
=(x+y-1-xy)(x+y-1-xy)
=(x+y-1-xy)^2

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

2x^2-5xy+2y^2+7x-5y+3
=(x-2y+3)(2x-y+1)

设：
x²+xy+ky²-2x+11y-15
=(x+ay+b)(x+cy+d)
=x^2+cxy+dx+axy+acy^2+ady+bx+bcy+bd
=x^2+(c+a)xy+acy^2+(d+b)x+(ad+bc)y+bd
与上对比，得：
c+a=1
ac=k
d+b=-2
ad+bc=11
bd=-15
解得：
b=-5 d=3或b=3,d=-5
a=(11-b)/(d-b)
a=2,a=-1
a=2时，c=-1 k=-2
a=-1时，c=2 k=-2
因此，k=-2

(6x-9)y=7-4x
y=(7-4x)/(6x-9)
=(1+6-4x)/(6x-9)
=1/(6x-9)-2/3
1/(6x-9)=某整数n+2/3
1/(6x-9)=n+2/3=(3n+2)/3
1/(2x-3)=3n+2

x=(9n+6+1)/(6n+4)
=3/2+1/(6n+4)
1/(6n+4)=某整数m+1/2
n=-(4m+3)/(6m+3)=-2/3-1/(6m+3)
要是整数，只能m=0 ,此时，n=-1
1/(6x-9)=2/3-1=-1/3 x=1
y=-1
方程的整数解为x=1,y=-1
7月W7

Answer 4

x=4