Question

-Chứng minh -4x²+4x-12<0 với mọi x.

Answer 1

\(-4x^2+4x-12< 0 \)
\(\Leftrightarrow-\left(4x^2-4x+1\right)-11< 0\)
\(\Leftrightarrow-\left(2x-1\right)^2-11< 0\left(đpcm\right)\)

Answer 2

Ta có:   \(-4x^2+4x-12=-\left(2x\right)^2+4x-1-11\)=\(\left[-\left(2x\right)^2+4x-1\right]-11\)

             \(=-\left(2x-1\right)^2-11\)

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

\(-\left(2x-1\right)^2< 0\)\(\forall x\)

\(-\left(2x-1\right)^2-11< -11< 0\)\(\forall x\)

hay \(-4x^2+4x-12< 0\)\(\forall x\)