Question

在线等！解方程1/(X-5)+2/(X-4)+3/()X-3+4/(X-2)=4

解方程
1/(X-5)+2/(X-4)+3/()X-3+4/(X-2)=4

Answer 1

1/(X-5)+2/(X-4)+3/(X-3)+4/(X-2)=1+1+1+1
[1-1/(X-5)]+[1-2/(X-4)]+[1-3/(X-3)]+[1-4/(X-2)]=0
(X-6)/(X-5)+(X-6)/(X-4)+(X-6)/(X-3)+(X-6)/(X-2)=0
(X-6)[1/(X-5)+1/(X-4)+1/(X-3)+1/(X-2)]=0
(X-6)[(2X-7)/(X-5)(X-2)+(2X-7)/(X-3)(X-4)]=0
(X-6)(2X-7)[1/(X^2-7X+10)+1/(X^2-7X+12)]=0
先求出两个解X=6,X=7/2
1/(X^2-7X+10)+1/(X^2-7X+12)=0
令Y=X^2-7X
1/(Y+10)+1/(Y+12)=0
(2Y+22)/(Y+10)(Y+12)=0
所以Y=-11
X^2-7X=-11
X=(7-√5)/2,X=(7+√5)/2
所以一共有4个解
X=6,X=7/2,X=(7-√5)/2,X=(7+√5)/2

Answer 2

aa

Answer 3

你写错了，不是：1/(X-5)+2/(X-4)+3/()X-3+4/(X-2)=4
而是：1/(X-5)+2/(X-4)+3/(X-3）+4/(X-2)=4