4(x-1)^2=9(x-5)^2
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4(x-1)^2=9(x-5)^24(x-1)^2=9(x-5)^24(x-1)^2=9(x-5)^2两边同时开平方,但要注意分类讨论(正负号):2(x-1)=+/-3(x-5)1:2x-2=3x-1
4(x-1)^2=9(x-5)^2
4(x-1)^2=9(x-5)^2
4(x-1)^2=9(x-5)^2
两边同时开平方,但要注意分类讨论(正负号):
2(x-1)=+/-3(x-5)
1:2x-2=3x-15
x1=13
2:2x-2=-3x+15
5x=17
x2=17/5
所以x1=13,x2=17/5.
等式等价变换为:(X-1)/(X-5)=1.5 或 (X-1)/(X-5)=-1.5
解得:X=13或X=17/5
逆用平方差公式
4(x-1)^2=9(x-5)^2
[2(x-1)]^2-[3(x-5]^2=0
[2(x-1)+3(x-5)][2(x-1)-3(x-5)]=0
(5x-17)(-x+13)=0
5x-17=0或-x+13=0
所以x1=5/17,x2=13
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