Question

Chứng minh rằng đa thức : \(x^2-2x+2\) vô nghiệm

Answer 1

\(x^2-2x+2=x^2-2x+1+1=\left(x-1\right)^2+1=>\left(x-1\right)^2=-1\left(vônghiemej\right)\)

Answer 2

\(x^2-2x+2\)

\(=x^2-x-x+1+1\)

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

\(=x\left(x-1\right)-\left(x-1\right)+1\)

\(=\left(x-1\right)\left(x-1\right)+1\)

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

\(\left(x-1\right)^2\ge0\forall x\Rightarrow\left(x-1\right)^2+1\ge1\forall x\)

\(\Rightarrow\left(x-1\right)^2+1>0\forall x\)

Vậy đa thức x² - 2x + 2 vô nghiệm