Question

CMR: 4x^2 - 4x +3 > 0 với mọi x

Answer 1

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

 

Answer 2

\(\text{Ta có : }4x^2-4x+3\\ \\ =4x^2-4x+1+2\\ \\ =\left(4x^2-4x+1\right)+2\\ \\ =\left(2x-1\right)^2+2\\ Do\left(2x-1\right)^2\ge0\forall x\\ \Rightarrow\left(2x-1\right)^2+2\ge2\forall x\\ \Rightarrow\left(2x-1\right)^2+2>0\forall x\left(đpcm\right)\)

Vậy \(4x^2-4x+3>0\forall x\)