Question

Giải phương trình:

\(x^4 – 2x^3 + 3x^2 – 2x +1 = 0 \)

Answer 1

\(x^4-2x^3+3x^2-2x+1=0\)

\(\Leftrightarrow\left(x^2-x+1\right)^2=0\)

\(\Leftrightarrow\left(x^2-x+\dfrac{1}{4}+\dfrac{3}{4}\right)^2=0\)

\(\Leftrightarrow\left[\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}\right]^2=0\)

\(\Leftrightarrow\left[\left(x-\dfrac{1}{2}\right)^2\right]^2+\left(\dfrac{3}{4}\right)^2>0\forall x\)

Vô nghiệm

Answer 2

\(\left(x^4+x^2-2x^3-2x+1\right)=\left(x^2-x+1\right)^2=0\)

\(\Rightarrow x^2-x+1=0\Leftrightarrow\left(x-\dfrac{1}{2}\right)^2+\dfrac{3}{4}=0\Rightarrow vo.N_o\)

Answer 3

số đẹp thế :V