用因式分解法解下列方程1.（x-4)²+19（x-4)-20=02.(2x-5)²-9（x-2)²=03.2（t-1)²+t=04.3(1-x)²-5(x-1)-2=05.[x/(x²-x)]+2=2x/(x+1)

Question

用因式分解法解下列方程
1.（x-4)²+19（x-4)-20=0
2.(2x-5)²-9（x-2)²=0
3.2（t-1)²+t=0
4.3(1-x)²-5(x-1)-2=0
5.[x/(x²-x)]+2=2x/(x+1)

Answer 1

1.（X-4+20)(X-4-1)=0 (X+15)(X-5)=0 X1=-15 X2=5
2.4X²-20X+25-9X²+36X-36=0 -5X²+16X-11=0 (-5X-11)(X+1)=0
X1=-11/5 X=-1
3.2t²-4t+2+t=0 2t²-3t+2=0 用求根公式
4.3-6X+3X²-5X+5-2=0 3X²-11X+6=0 (X-3)(3X-2)=0 X1=3 X2=2/3
5.1/（X-1)+2=2X/(X+1)
两边乘于X²-1 X+1+2X²-2=2X(X-1) 3X-1=0 X=1/3