Question

Tính GTNN của biểu thức 

B= x.(2x-1)

C=x.(3x+4)

Answer 1

\(B=x\left(2x-1\right)=2x^2-x=2\left(x^2-\dfrac{1}{2}x+\dfrac{1}{16}\right)-\dfrac{1}{8}=2\left(x-\dfrac{1}{4}\right)^2-\dfrac{1}{8}\ge-\dfrac{1}{8}\)

\(minB=-\dfrac{1}{8}\Leftrightarrow x=\dfrac{1}{4}\)

\(C=x\left(3x+4\right)=3x^2+4x=3\left(x^2+\dfrac{4}{3}x+\dfrac{4}{9}\right)-\dfrac{4}{3}=3\left(x+\dfrac{2}{3}\right)^2-\dfrac{4}{3}\ge-\dfrac{4}{3}\)

\(minC=-\dfrac{4}{3}\Leftrightarrow x=-\dfrac{2}{3}\)

Answer 2

`B=x(2x-1)`

`=2x(x-1/2)`

`=2(x^2-1/2x)`

`=2(x^2-1/2x+1/16)-1/8`

`=2(x-1/4)^2-1/8>=-1/8`

Dấu "=" xảy ra khi `x=1/4`

`C=x(3x+4)`

`=3x(x+4/3)`

`=3(x^2+4/3x)`

`=3(x^2+4/3x+4/9)-4/3`

`=3(x+2/3)^2-4/3>=-4/3`

Dấu "=" xảy ra khi `x=-2/3`