Question

ai nhanh mik tik (ai k mik  mik k lại)

Cm: biểu thức sau luôn luôn âm

 -5x^2+20x-49

Answer 1

\(-5x^2+20x-49=-5\left(x^2-4x+\frac{49}{5}\right)=-5\left(x^2-2.x.2+4+\frac{29}{5}\right)\)

                                                                                   \(=-5\left(x-2\right)^2-\frac{29}{5}=\frac{-29}{5}-5\left(x-2\right)^2\)

Vì \(\left(x-2\right)^2\ge0\Rightarrow5\left(x-2\right)^2\ge0\)

Suy ra: \(\frac{-29}{5}-5\left(x-2\right)^2\le\frac{-29}{5}< 0\)

Vậy ...........