a) \(A=x^4+4x+7=\left(x^2+4x+4\right)+3=\left(x+2\right)^2+3\ge3\)

\(minA=3\Leftrightarrow x=-2\)

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

\(minB=\dfrac{3}{4}\Leftrightarrow x=\dfrac{1}{2}\)

c) \(C=4x-x^2+3=-\left(x^2-4x+4\right)+7=-\left(x-2\right)^2+7\le7\)

\(maxC=7\Leftrightarrow x=2\)

d) \(D=2x-2x^2-5=-2\left(x^2-x+\dfrac{1}{4}\right)-\dfrac{9}{2}=-2\left(x-\dfrac{1}{2}\right)^2-\dfrac{9}{2}\le-\dfrac{9}{2}\)

\(maxD=-\dfrac{9}{2}\Leftrightarrow x=\dfrac{1}{2}\)

Bài 5:

\(a,\dfrac{2}{2x-4}=\dfrac{2}{2\left(x-2\right)}=\dfrac{1}{x-2};\dfrac{3}{3x-6}=\dfrac{3}{3\left(x-2\right)}=\dfrac{1}{x-2}\\ b,\dfrac{1}{x+4}=\dfrac{2\left(x-4\right)}{2\left(x+4\right)\left(x-4\right)};\dfrac{1}{2x+8}=\dfrac{x-4}{2\left(x+4\right)\left(x-4\right)}\\ \dfrac{3}{x-4}=\dfrac{6\left(x+4\right)}{2\left(x-4\right)\left(x+4\right)}\\ c,\dfrac{1}{x^2-1}=\dfrac{1}{\left(x-1\right)\left(x+1\right)};\dfrac{2}{x-1}=\dfrac{2\left(x+1\right)}{\left(x-1\right)\left(x+1\right)}\\ \dfrac{2}{x+1}=\dfrac{2\left(x-1\right)}{\left(x-1\right)\left(x+1\right)}\\ d,\dfrac{1}{2x}=\dfrac{x-2}{2x\left(x-2\right)};\dfrac{2}{x-2}=\dfrac{4x}{2x\left(x-2\right)};\dfrac{3}{2x\left(x-2\right)}\text{ giữ nguyên}\)

Bài 4:

\(a,\dfrac{x^2-4x+4}{x^2-2x}=\dfrac{\left(x-2\right)^2}{x\left(x-2\right)}=\dfrac{x-2}{x}=\dfrac{\left(x-2\right)\left(x-1\right)}{x\left(x-1\right)}\\ \dfrac{x+1}{x^2-1}=\dfrac{1}{x-1}=\dfrac{x}{x\left(x-1\right)}\\ b,\dfrac{x^3-2^3}{x^2-4}=\dfrac{\left(x-2\right)\left(x^2+2x+4\right)}{\left(x-2\right)\left(x+2\right)}=\dfrac{x^2+2x+4}{x+2};\dfrac{3}{x+2}\text{ giữ nguyên}\)

h) \(=8-12y+6y^2-y^3\)

i) \(=8y^3-125\)

j) \(=27y^3+64\)

k) \(=x^3-9x^2+27x-27+8-12x+6x-x^3=-9x^2+21x-19\)

Hướng dẫn: A đạt GTLN khi \(\dfrac{1}{A}\) đạt GTNN

Ta có: \(x^2+2\ge0\forall x\)

\(\Rightarrow A=\dfrac{1}{x^2+2}\le\dfrac{1}{2}\forall x\)

Vậy GTLN của A là 1/2

=> A

Câu 2: B đạt GTLN khi và chỉ khi x² đạt giá trị nhỏ nhất

⇔ x²=0 ⇒B = 10 - 0= 0 

  Chọn đáp án B nhe

Câu 3: Có A= 4x - 2x²= (-2x² + 4x - 1) + 1=\(-2\left(x^2-2x+1\right)+1\)

⇔ A= \(-2\left(x-1\right)^2+1\le1\)

Chọn đáp án B nha

Bài 4

Ta có: \(\left(4+2x\right)\left(4-2x\right)+\left(2x-3\right)^2=2\)

\(\Leftrightarrow16-4x^2+4x^2-12x+9=2\)

\(\Leftrightarrow-12x=-23\)

hay \(x=\dfrac{23}{12}\)

Ta có:

AE vuông góc BD

CF vuông góc BD

=> AE//CF(1)

Xét 2 tam giác vuông AED và CFB có:

AD=BC

góc ADB = góc CBF ( 2 góc slt)

=> tam giác AED = tam giác CFB (ch-gn)

=> AE= CF (2)

Từ (1) và (2) => AECF là hbh ( đpcm)