1) x3−x2=4x2−8x+4⇔x3−x2−4x2+8x−4=0
⇔x3−4x2+4x−x2+4x−4=0
x(x2−4x+4)−(x2−4x+4)=0⇔(x−1)(x2−4x+4)=0
⇔(x−1)(x−2)2=0⇔(x−1)(x−2)(x−2)=0
⇔⎣⎡x−1=0x−2=0x−2=0 ⇔⎣⎡x=1x=2x=2 vậy x=1;x=2
2) 9x2−49=0⇔(3x)2−72=0⇔(3x−7)(3x+7)=0
⇔[3x−7=03x+7=0 ⇔[3x=73x=−7 ⇔⎣⎢⎡x=37x=3−7 vậy x=37;x=3−7 3) x2−9=5(x−3)2⇔x2−9=5(x2−6x+9)
5x2−30x+45=x2−9⇔5x2−30x+45−x2+9=0
⇔4x2−30x+54=0⇔4x2−12x−18x+54=0
⇔4x(x−3)−18(x−3)=0⇔(4x−18)(x−3)=0
⇔[4x−18=0x−3=0 ⇔[4x=18x=3 ⇔[x=418=29x=3 vậy x=29;x=3