Question

Tìm GTNN của:

A=x(x-6)

B=2x^2+7x-2

C= 3x^2-6x-1

D=x^2+x-1

Answer 1

\(A=x^2-6x=x^2-6x+9-9=\left(x-3\right)^2-9\Rightarrow minA=-9\)

\(B=2x^2+7x-2=2\left(x^2+2\cdot\frac{7}{4}x+\frac{49}{16}\right)-\frac{65}{8}=2\left(x+\frac{7}{4}\right)^2-\frac{65}{8}\Rightarrow minB=-\frac{65}{8}\)

\(C=3x^2-6x-1=3\left(x^2-2x+1\right)-4=3\left(x-1\right)^2-4\Rightarrow minC=-4\)

\(D=x^2+x-1=\left(x^2+2x\cdot\frac{1}{2}+\frac{1}{4}\right)-\frac{5}{4}=\left(x+\frac{1}{2}\right)^2-\frac{5}{4}\Rightarrow minD=-\frac{5}{4}\)