\(4x^2-4x+2=4x^2-2x-2x+2\\ =2x\left(2x-1\right)-2x+1+1=2x\left(2x-1\right)-\left(2x-1\right)+1\\ =\left(2x-1\right)\cdot\left(2x-1\right)+1\\ =\left(2x-1\right)^2+1\\ Vì\left(2x-1\right)^2\ge0\forall x\Rightarrow\left(2x-1\right)^2+1\ge1\forall x\\ \RightarrowĐathứcvônghiệm\\ \RightarrowĐpcm\)