Question

chứng minh rằng: x^2-2√2x+2>=0 với mọi x

Answer 1

\(x^2-2\sqrt{2}x+2=\left(x-\sqrt{2}\right)^2\ge0\)

Answer 2

\(x^2-2\sqrt{2}x+2=x^2-2\sqrt{2}x+\left(\sqrt{2}\right)^2=\left(x-\sqrt{2}\right)^2\)

vì \(\left(x-\sqrt{2}\right)^2\ge0\forall x\)\(\Rightarrow\)\(x^2-2\sqrt{2}x+2\ge0\forall x\)