解方程x^2+9x^2/(x-3)^2=16

解方程x^2+9x^2/(x-3)^2=16
解方程x^2+9x^2/(x-3)^2=16

解方程x^2+9x^2/(x-3)^2=16
原方程为:x^2+[3x/(x-3)]^2=16
对方程左边进行配方:x^2+2x*3x/(x-3)+[3x/(x-3)]^2=16+2x*3x/(x-3)
合并移项得到:[x+ 3x/(x-3)]^2- 6x^2/(x-3)-16=0
[ x^2/(x-3) ]^2- 6x^2/(x-3)-16=0
把x^2/(x-3) 看作一整体,该方程可因式分解成:
[x^2/(x-3)-8][x^2/(x-3)+2]=0
即x^2/(x-3)-8=0 x^2/(x-3)+2=0
解这两方程,第一方程无解.第二方程的解为:
x1=-1+根号下7 x2=-1-根号下7