x平方加x加1的平方分之x平方等于3步骤答案.x²+x²/(x+1)²=3

x²+x²/(x+1)²=3设t＝x+1 x=t-1(t-1)²+(t-1)²/t²=3t²-2t+1+1-2/t+1/t²=3t²+2+1/t²-2t-2/t²=3(t+1/t)²-2(t-1/t)=3 令y＝t+1/ty²-2y-3=0(y-3)(y+1)=0y=3 y=-1x+1+1/(x+1)=3(x+1)²+1=3x+3x²+2x+2=3x+3x²-x-1=0(x-1/2)²-5/4=0x-1/2=±√5/2x=1/2±√5/2x+1+1/(x+1)=-1(x+1)²+1=-x-1x²+2x+2=-x-1x²+3x+3=0无解 所以 x=1/2±√5/2