Đáp án:
Giải thích các bước giải:
10.
x4+2x3-2x2+2x-3=0
⇔ x3(x-1) +3x2(x-1) +x(x-1)+3(x-1)=0
⇔(x-1)(x3+3x2+x+3)=0
⇒x-1=0 hoac x3+3x2+x+3=0
+) x-1=0⇔x=1
+)x3+x+3x2+3=0
⇔x(x2+1)+3(x2+1)=0
⇔(x+1)(x2+1)=0
⇔x+1=0 ( Vi x2+1>0 ∀x)
⇔x=-1
Vay...
11.
2x3+7x2+7x+2=0
⇔2x2(x+1) + 5x(x+1)+2(x+1)=0
⇔(x+1)(2x2+5x+2)=0
⇒x+1=0 hoac 2x2+5x+2=0
+) x+1=0⇔x=-1
+)2x2+5x+2=0
Δ=25-4*2*2=9>0
⇒Phuong trinh co hai nghiem phan biet x1=-5-√Δ /2*2=-2
x2=-5+√Δ /2*2=-1/2
Vay...
12.
x4-3x3+4x2-3x+1=0
⇔x3(x-1)-2x2(x-1)+2x(x-1)-(x-1)=0
⇔(x-1)(x3-2x2+2x-1)=0
⇔(x-1)[x2(x-1)-x(x-1)+(x-1)]=0
⇔(x-1)^2(x2-x+1)=0 ( Vi x2-x+1 >0 ∀x)
⇔(x-1)^2=0
⇔x-1=0
⇔x=1
Vay..
