X2 3(x^2+1)/(x+2)=4(x+2)/(x^2+1)+4用换元法怎么解

3(x^2+1)/(x+2)=4(x+2)/(x^2+1)+4用换元法怎么解  

3(x^2+1)/(x+2)=4(x+2)/(x^2+1)+4用换元法怎么解

令a=(x²+1)/(x+2)
则3a=4/a+4
3a²-4a-4=0
(3a+2)(a-2)=0
a=-2/3,a=2
(x²+1)/(x+2)=-2/3
3x²+3=-2x-4
3x²+2x+7=0
△<0
无解
(x²+1)/(x+2)=2
x²+1=2x+4
x²-2x-3=0
(x+1)(x-3)=0
x=-1,x=3

换元法解方程⑴ 2（x^2+1）/（x+1）+6（x+1）/（x^2+1）=7 ⑵（x^4+2x^2+1）/(x^2)+（x^2+1）/x=2需步骤

换元法解方程⑴ 2（x^2+1）/（x+1）+6（x+1）/（x^2+1）=7
令（x^2+1）/（x+1）=t
2t+6/t=7
2t^2-7t+6=0
(2t-3)(t-2)=0
t=3/2或t=2
(1)t=3/2
（x^2+1）/（x+1）=3/2
2（x^2+1）=3（x+1）
2x^2+2=3x+3
2x^2-3x-1=0
x=(3±√3^2+4*2*1)/2*2=(3±√17)/4
(2)t=2
（x^2+1）/（x+1）=2
（x^2+1）=2（x+1）
x^2+1-2x-2=0
x^2-2x-1=0
x=(2±√2^2+4*1*1)/2*1=(1±√2)
⑵（x^4+2x^2+1）/(x^2)+（x^2+1）/x=2
(x^2+1)^2/(x^2)+（x^2+1）/x=2
(x^2+1/x)^2+（x^2+1）/x=2
令x^2+1/x=t
t^2+t=2
t^2+t-2=0
(t-1)(t+2)=0
t=1或t=-2
(1)t=1
x^2+1/x=1
x^2+1=x
x^2-x+1=0
判别式=1^2-4*1*1=-3<0
所以方程无解
(2)t=-2
x^2+1/x=-2
x^2+1=-2x
x^2+2x+1=0
(x+1)^2=0
所以x=-1

用换元法求∫dx/x∧2√(x∧2+1)）

这两个答案是相同的吧
令
x^2 = sec^2 t = tan^2 t+1
t = arcsec x = arctan √(x^2-1)
所以
arcsec x = arctan √(x^2-1)

x=tanu
∫dx/（x∧2√(x∧2+1)=∫dtanu/[tan²u√(tan²u+1)]
=∫secu/[tan²udu=∫cosu/sin²udu
=∫1/sin²udsinu=-1/sinu+C=-secu/tanu+C
=-√(x²+1)/x+C

用换元法解方程3(x+1)/x^2+1 + x^2+1/x+1=7/2

令a=x^2+1/x+1
∴3/a+a=7/2
6+a²=7a
a²-7a+6=0
(a-1)(a-6)=0
∴a1=1
a2=6

x^2+1/x+1=1 x^2+1/x+1=6
x²+1=x+1 x²+1=6x+6
x²-x=0 x²-6x-5=0
x(x-1)=0 x=[6±√(36+20)]/4
∴x1=0 x2=1 x3=(3±√14)/2

2(x/x+2)平方+(x/x+2)=3 用换元法

2(x/x+2)平方+(x/x+2)=3
设x/(x+2)=y,则
2y^2+y-3=0
(2y+3)(y-1)=0
y=-3/2或y=1
由x/(x+2)=-3/2,解之得x=-6/5
由x/(x+2)=1,解之得x无解
所以x=-6/5

已知f[(x+1)/x]=(x^2+1)/(x^2)+1/x求f（x）换元法！

令a=1/x
则(x+1)/x=1+1/x=1+a
(x²+1)/x²+1/x
=1+1/x²+1/x
=1+a²+a
所以f(1+a)=a²+a+1
令x=1+a
a=x-1
所以f(x)=(x-1)²+(x-1)+1
即f(x)=x²-x+1

用换元法解方程(x-1)/(x+2)-3/(x-1)-1=0

(x-1)/(x+2)-3/(x-1)-1=0
(x-1)/(x+2)-[(x+2)-(x-1)]/(x-1)-1=0
(x-1)/(x+2)-(x+2)/(x-1)+1-1=0
(x-1)/(x+2)-(x+2)/(x-1)=0
设(x-1)/(x+2)=y，则y-1/y=0
即：y²-1=0，解得：y1=1 y2=-1
即：(x-1)/(x+2)=1，或者(x-1)/(x+2)=-1
解得：x=-1/2
经检验是原方程的根

x^4+x^2+1/x^4+1/x^2=4 解X 换元法

x^4+x^2+1/x^4+1/x^2=4
x^4+1/x^4+x^2+1/x^2-4=0
(x^4+1/x^4-2)+(x^2+1/x^2-2)=0
(x^2-1/x^2)^2+(x-1/x)^2=0
所以x-1/x=0
x^2-1/x^2=0
解得x=±1

（2x-1)/3=(x+2)/2+1 求X

等式两边乘6
得 2（2x-1）=3(x+2)+6
4x-2=3x+6+6
4x-2=3x+12
x=12+2=14