Tìm GTNN :
\(B=x^2-x\)
\(B=x^2-2\cdot x\cdot\frac{1}{2}+\frac{1}{4}-\frac{1}{4}\)
\(B=\left(x-\frac{1}{2}\right)^2-\frac{1}{4}\ge\frac{-1}{4}\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x=\frac{1}{2}\)
\(C=2x^2+8x\)
\(C=2\left(x^2+4x\right)\)
\(C=2\left(x^2+4x+4-4\right)\)
\(C=2\left[\left(x+2\right)^2-4\right]\)
\(C=2\left(x+2\right)^2-8\ge-8\forall x\)
Dấu "=" xảy ra \(\Leftrightarrow x=-2\)
Tìm x :
\(\left(x-3\right)^3-x\left(x+1\right)\left(x-1\right)+6x^2=6\)
\(\Leftrightarrow x^3-9x^2+27x-27-x\left(x^2-1\right)+6x^2-6=0\)
\(\Leftrightarrow-3x^2+28x-33=0\)
\(\Leftrightarrow-3\left(x^2-\frac{28}{3}x+11\right)=0\)
\(\Leftrightarrow x^2-2\cdot x\cdot\frac{14}{3}+\frac{196}{9}-\frac{97}{9}=0\)
\(\Leftrightarrow\left(x-\frac{14}{3}\right)^2=\left(\frac{\pm\sqrt{97}}{3}\right)^2\)
\(\Leftrightarrow x=\frac{\pm\sqrt{97}+14}{3}\)
