Question

Tìm GTNN

B= -14+2X^2+X

Answer 1

B=2(x^2+2.x.1/4 +1/16)^2 -57/8

  =2.(x+1/4)^2 -57/8

MinB=-57/8 khi x=-1/4

Answer 2

\(B=-14+2x^2+x=2\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)-\dfrac{113}{8}=2\left(x+\dfrac{1}{4}\right)^2-\dfrac{113}{8}\ge-\dfrac{113}{8}\)\(ĐTXR\Leftrightarrow x=-\dfrac{1}{4}\)

Answer 3

\(B=2x^2+x-14\)

\(=2\left(x^2+\dfrac{1}{2}x-7\right)\)

\(=2\left(x^2+2\cdot x\cdot\dfrac{1}{4}+\dfrac{1}{16}-\dfrac{113}{16}\right)\)

\(=2\left(x+\dfrac{1}{4}\right)^2-\dfrac{113}{8}\ge-\dfrac{113}{8}\forall x\)

Dấu '=' xảy ra khi \(x=-\dfrac{1}{4}\)