Cách 2 :

Ta có : \(\dfrac{a+b}{2}=1\Rightarrow a+b=2\)

Mặt khác : Với \(\forall a,b\) thì : \(a^2+b^2\ge2ab\)

\(\Rightarrow2\left(a^2+b^2\right)\ge\left(a+b\right)^2=4\)

\(\Rightarrow2a^2+2b^2+2008\ge2012\)

\(\Rightarrow\dfrac{2011}{2a^2+2b^2+2008}\le\dfrac{2011}{2012}\)

Dấu '' = '' xảy ra khi a = b = 1

Vậy GTLN của biểu thức là \(\dfrac{2011}{2012}\Leftrightarrow a=b=1\)

a, Ta có : \(\dfrac{98x^2-2}{x-2}=0\Leftrightarrow\left\{{}\begin{matrix}98x^2-2=0\\x-2\ne0\end{matrix}\right.\)

hay \(\left\{{}\begin{matrix}x^2=\dfrac{1}{49}\\x\ne2\end{matrix}\right.\Leftrightarrow x=\pm\dfrac{1}{7}\)

Vậy giá trị của phân thức này bằng 0 khi \(x=\pm\dfrac{1}{7}\)

b, Ta có : \(\dfrac{3x-2}{x^2+2x+1}=0\Leftrightarrow\dfrac{3x-2}{\left(x+1\right)^2}=0\Leftrightarrow\left\{{}\begin{matrix}3x-2=0\\\left(x+1\right)^2\ne0\end{matrix}\right.\)

hay \(\left\{{}\begin{matrix}x=\dfrac{2}{3}\\x\ne-1\end{matrix}\right.\)

Vậy giá trị của phân thức này bằng 0 khi \(x=\dfrac{2}{3}\)

Ta có : \(B=\left(2x\right)^2-2.2x\left(y-3\right)+\left(y-3\right)^2-\left(y-3\right)^2+y^2-6y+16\)

\(=\left(2x-y+3\right)^2-y^2+6y-9+y^2-6y+16\)

\(=\left(2x-y+3\right)^2+7\)

Vì \(\left(2x-y+3\right)^2\ge0\forall x,y\Rightarrow B\ge7\)

hay B > 0 với mọi x,y

Ta có : \(\left(a+b+c\right)^2=a^2+b^2+c^2\)

\(\Rightarrow a^2+b^2+c^2+2\left(ab+bc+ca\right)-a^2-b^2-c^2=0\)

\(\Rightarrow ab+bc+ca=0\)

\(\Rightarrow a^3b^3+b^3c^3+c^3a^3=3a^2b^2c^2\)

Chia cả 2 vế cho \(a^3b^3c^3\) , ta có :

\(\dfrac{1}{a^3}+\dfrac{1}{b^3}+\dfrac{1}{c^3}=\dfrac{3}{abc}\left(đpcm\right)\)

\(C=\dfrac{2}{x^2+4x+5}=\dfrac{2}{\left(x+2\right)^2+1}\)

Vì \(\left(x+2\right)^2\ge0\Rightarrow\left(x+2\right)^2+1\ge1\)

\(\Rightarrow C\le2\)

Dấu ''='' xảy ra \(\Leftrightarrow x=-2\)

Vậy Min C = 2 kjhi x = -2

608:8x35=2660

Ta có : A = \(11^{n+2}+12^{2n+1}\)

= \(11^n.121+\left(12^2\right)^n.12\)

= \(11^n.133-11^n.12+144^n.12\)

= \(11^n.133+12\left(144^n-11^n\right)\)

Vì \(\left\{{}\begin{matrix}11^n.133⋮133\\12\left(144^n-11^n\right)⋮133\end{matrix}\right.\Rightarrow A⋮133\left(đpcm\right)\)

tớ nhầm nha . câu 5 là :

Miss Thuy is washing her hair now because she will go to a party tonight.

1. She doesn't have much time to write to her friends .

2. Have your mother ever traveled to work by bus ?

3. Hoa's sister is listening to music in her room at the moment .

4. My brother lives in Paris and has a bakery there .

5. Miss Thuy is washing her hair because she will go to the party tonight