a) \(A=x^2+3x+4=\left(x+\dfrac{3}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\)

\(minA=\dfrac{7}{4}\Leftrightarrow x=-\dfrac{3}{2}\)

b) \(B=2x^2-x+1=2\left(x-\dfrac{1}{4}\right)^2+\dfrac{7}{8}\ge\dfrac{7}{8}\)

\(minB=\dfrac{7}{8}\Leftrightarrow x=\dfrac{1}{4}\)

c) \(C=5x^2+2x-3=5\left(x+\dfrac{1}{5}\right)^2-\dfrac{16}{5}\ge-\dfrac{16}{5}\)

\(minC=-\dfrac{16}{5}\Leftrightarrow x=-\dfrac{1}{5}\)

d) \(D=4x^2+4x-24=\left(2x+1\right)^2-25\ge-25\)

\(minD=-25\Leftrightarrow x=-\dfrac{1}{2}\)

e) \(E=x^2+6x-11=\left(x+3\right)^2-20\ge-20\)

\(minE=-20\Leftrightarrow x=-3\)

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

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

a: Ta có: \(A=x^2+3x+4\)

\(=x^2+2\cdot x\cdot\dfrac{3}{2}+\dfrac{9}{4}+\dfrac{7}{4}\)

\(=\left(x+\dfrac{3}{2}\right)^2+\dfrac{7}{4}\ge\dfrac{7}{4}\forall x\)

Dấu '=' xảy ra khi \(x=-\dfrac{3}{2}\)

d: Ta có: \(D=4x^2+4x-24\)

\(=4x^2+4x+1-25\)

\(=\left(2x+1\right)^2-25\ge-25\forall x\)

Dấu '=' xảy ra khi \(x=-\dfrac{1}{2}\)

e: ta có: \(E=x^2+6x-11\)

\(=x^2+6x+9-20\)

\(=\left(x+3\right)^2-20\ge-20\forall x\)

Dấu '=' xảy ra khi x=-3

vâng ạ

x=-3

y=-5

z=-1

\(A=\left|x+\frac{2}{3}\right|\)

Ta có: \(\left|x+\frac{2}{3}\right|\ge0\forall x\)

\(A=0\Leftrightarrow\left|x+\frac{2}{3}\right|=0\Leftrightarrow x=-\frac{2}{3}\)

Vậy \(A_{min}=0\Leftrightarrow x=-\frac{2}{3}\)

\(B=\left|x\right|+\frac{1}{2}\)

Ta có: \(\left|x\right|\ge0\forall x\)

\(\Rightarrow\left|x\right|+\frac{1}{2}\ge\frac{1}{2}\forall x\)

\(B=\frac{1}{2}\Leftrightarrow\left|x\right|=0\Leftrightarrow x=0\)

Vậy \(B_{min}=\frac{1}{2}\Leftrightarrow x=0\)

Câu c,d tương tự

P/S tất cả những bài trên chỉ tìm được min, ko tìm được max. 

ma ban oi, cau e va f thi sao

câu trả lời của mình ở trong này nè. nếu thấy đúng thì **** luôn nha

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