2. 

\(\left(x\pm\dfrac{4}{3}\right)^{2000}\ge0\forall x\\ =>B\ge105\)

Dấu ''='' xảy ra `<=>` \(x=\mp\dfrac{4}{3}\)

Vậy GTNN `=105<=>` \(x=\mp\dfrac{4}{3}\)

3. \(\left(x+\dfrac{3}{8}\right)^{442}\ge0\forall x\\ =>-\left(x+\dfrac{3}{8}\right)^{442}\le0\\ =>B\le-\dfrac{2}{3}\)

Dấu ''='' xảy ra `<=>x=-3/8`

Vậy GTLN `=-2/3<=>x=-3/8`

a: \(B=\left(x+1\right)^2-2\left(x+1\right)+1+0.01\)

\(=x^2+0.01>0\)

b: \(B_{MIN}=0.01\)

Dấu '=' xảy ra khi x=0

\(=2\left(\dfrac{1}{3}-\dfrac{1}{5}+\dfrac{1}{5}-\dfrac{1}{7}+...+\dfrac{1}{15}-\dfrac{1}{17}\right)\)

\(=2\cdot\dfrac{14}{51}=\dfrac{28}{51}\)

a: =>(x-5)(2x+3)=0

=>x=5 hoặc x=-3/2

b: =>(x-4)(x+4)=0

=>x=4 hoặc x=-4

e) \(\sqrt{4-\sqrt{7}}-\sqrt{4+\sqrt{7}}+\sqrt{2}\)

\(=\dfrac{\sqrt{8-2\sqrt{7}}}{\sqrt{2}}-\dfrac{\sqrt{8+2\sqrt{7}}}{\sqrt{2}}+\sqrt{2}\)

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

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

\(=-\sqrt{2}+\sqrt{2}=0\)

\(=y^4+y^3-y^2-2y-\left(y^4+y^3+y^2-2y^2-2y-2\right)\)

\(=y^4+y^3-y^2-2y-y^4-y^3+y^2+2y+2=2\)

\(=3\left(x^2-2xy+y^2-4z^2\right)\)

\(=3\left(x-y-2z\right)\left(x-y+2z\right)\)

= 3(x² - 2xy + y² - 4z²)

= 3((x - y)² - 4z²)

= 3(x - y - 2z)(x - y + 2z)