Question

CMR các biểu thức sau có giá trị âm với mọi x

F=-3x^2-6x-4

Answer 1

\(F=-3x^2-6x-4=-\left(3x^2+6x+4\right)\)

\(=-3\left(x^2+2x+\dfrac{4}{3}\right)=-3\left(x^2+2x+1+\dfrac{1}{3}\right)\)

\(=-3\left[\left(x+1\right)^2+\dfrac{1}{3}\right]\)

\(do\) \(\left(x+1\right)^2\ge0=>\left(x+1\right)^2+\dfrac{1}{3}\ge\dfrac{1}{3}\)

\(=>-3\left[\left(x+1\right)^2+\dfrac{1}{3}\right]\le-1\)

\(=>-3\left[\left(x+1\right)^2+\dfrac{1}{3}\right]< 0\)\(=>F< 0\left(\forall x\right)\)