![](https://rs.olm.vn/images/avt/0.png?1311)
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^4-6x^3+16x^2-22x+16=0\)
\(\Rightarrow x^4-2x^3+3x^2-4x^3+8x^2-12x+5x^2-10x+15+1=0\)
\(\Rightarrow x^2\left(x^2-2x+3\right)-4x\left(x^2-2x+3\right)+5\left(x^2-2x+3\right)x^2+1=0\)
\(\Rightarrow\left(x^2-2x+3\right)\left(x^2-4x+5\right)=-1\)
\(\Rightarrow\left(x^2-2x+1+2\right)\left(x^2-4x+4+1\right)=-1\)
\(\Rightarrow\left[\left(x-1\right)^2+2\right]\left[\left(x-2\right)^2+1\right]=-1\left(1\right)\)
mà \(\left\{{}\begin{matrix}\left(x-1\right)^2+2>0,\forall x\\\left(x-2\right)^2+1>0,\forall x\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left[\left(x-1\right)^2+2\right]\left[\left(x-2\right)^2+1\right]>0,\forall x\\\left[\left(x-1\right)^2+2\right]\left[\left(x-2\right)^2+1\right]=-1\end{matrix}\right.\) (vô lí)
Vậy phương trình trên vô nghiệm (dpcm)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(2x^2-6x+7=0\)
\(\Rightarrow2x^2-6x+\frac{9}{2}+\frac{5}{2}=0\)
\(\Rightarrow2\left(x^2-3x+\frac{9}{4}\right)+\frac{5}{2}=0\)
\(\Rightarrow2\left(x-\frac{3}{2}\right)^2+\frac{5}{2}>0\)( vô nghiệm)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
Ta có:
\(VT=\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2-x+2\right)\)
\(pt\Leftrightarrow\left(x^2+1\right)\left(x^2-x+1\right)\left(x^2-x+2\right)=0\)
Mà:
\(x^2+1>0\)
\(x^2-x+1=\left(x-\frac{1}{2}\right)^2+\frac{3}{4}>0\)
\(x^2-x+2=\left(x-\frac{1}{2}\right)^2+\frac{7}{4}>0\)
Vậy pt vô nghiệm
![](https://rs.olm.vn/images/avt/0.png?1311)
x4-3x2+6x+13=0
<=>x4-4x2+4+x2+6x+9=0
<=>(x2-2)2+(x-3)2=0
Ta thấy x2-2 khác x-3
=>PT vô nghiệm
![](https://rs.olm.vn/images/avt/0.png?1311)
...=x^4+x^3+x^2+5x^2+5x+5=x^(x^2+x+1)+5(x^2+x+1)=(x^2+5)(x^2+x+1)>0 (pt vô nghiệm)
\(\Leftrightarrow x^4+x^3+x^2+5x^2+5x+5=0\)
\(\Leftrightarrow x^2\left(x^2+x+1\right)+5\left(x^2+x+1\right)=0\)
\(\Leftrightarrow\left(x^2+x+1\right)\left(x^2+5\right)=0\)
\(\Leftrightarrow x^2+x+1=0\Leftrightarrow\left(x+\frac{1}{2}\right)^2+\frac{3}{4}=0\Leftrightarrow\left(x+\frac{1}{2}\right)^2=-\frac{3}{4}\left(l\right)\)
hay \(x^2+5=0\Leftrightarrow x^2=-5\left(l\right)\)
\(v...S=\varnothing\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(x^2-6x+70=0\)
\(\Leftrightarrow x^2-6x+9+61=0\)
\(\Leftrightarrow\left(x-3\right)^2+61=0\)
\(\Leftrightarrow\left(x-3\right)^2=-61\) (vô lý)
-Vậy PT vô nghiệm.