2−x2=2−x ĐKXĐ: x ≤ 2
pt <=> x4−4x2+4=2−x
⇔x4−4x2+x+2=0
⇔x2(x2−4)+(x+2)=0
⇔x2(x−2)(x+2)+(x+2)=0
⇔(x+2)(x3−2x2+1)=0
⇔(x+2)(x3−x2−x2+1)=0
⇔(x+2)[x2(x−1)−(x2−1)]=0
⇔(x+2)[x2(x−1)−(x−1)(x+1)]=0
⇔(x+2)(x−1)(x2−x−1)=0
⇔⎣⎡x+2=0x−1=0x2−x−1=0
+) x + 2 = 0 <=> x = -2
+) x - 1 = 0 <=> x = 1
+) x2−x−1=0
⇔x2−2⋅21x+41−45=0
⇔(x−21)2=45
⇔⎣⎢⎡x−21=25x−21=−25⇔⎣⎢⎡x=25+1x=21−5
Thử lại thấy x = -2 không thỏa mãn
Vậy pt có 3 nghiệm: ⎣⎢⎢⎢⎡x1=1x2=25+1x3=21−5