\(x.x^2.x^3=64\)

\(\Rightarrow x^6=64\)

\(\Rightarrow x^6=2^6\)

\(\Rightarrow x=2;x=-2\)

Bài làm:

Ta có: \(x\cdot x^2\cdot x^3=64\)

\(\Leftrightarrow x^6=64=2^6\)

\(\Leftrightarrow\orbr{\begin{cases}x=2\\x=-2\end{cases}}\)

Vậy \(x\in\left\{-2;2\right\}\)

a) \(a>\sqrt{a}\Leftrightarrow a^2>a\)   

\(a^2-a>0\) 

\(a\left(a-1\right)>0\)   

\(\hept{\begin{cases}a>0\\a-1>0\end{cases}}\) 

\(\hept{\begin{cases}a>0\\a>1\end{cases}}\)    

\(\Rightarrow a>1\)           

b) 

\(a< \sqrt{a}\)    

\(a^2< a\)       

\(a^2-a< 0\)   

\(a\left(a-1\right)< 0\) 

\(\hept{\begin{cases}a>0\\a-1< 0\end{cases}}\)   

\(\hept{\begin{cases}a>0\\a< 1\end{cases}}\)

Let me tell you about my family. I live with my mum, my dad and my big sister. We live in ___. My mum’s name is___. She’s a best mom with me . She’s a English teacher. She’s short and slim, she’s got long, brown hair and brown eyes .She so cute anyway.She always make me smile although I sad with something.She can cook very well.I really love her dishes .She also teach me Math and Literature.Everyday I wake up with her voice !!. My dad’s name is__. He’s a designer . He’s tall and a little fat! He’s got short brown hair and blue eyes. He works in a bank.I always see a smile on his face.He really love play to footbal.Sometime I play with his.It's very funny,you must try with your dad!He so good for meeting.I wishes you can meet his.You will his right now. My sister ___is __ years old and she loves listening to music. She listens to music all the time! She’s got long brown hair and green eyes, me.She study at __school with me,too.So you can visit our school and play with her,also me!!. . We’ve got a pet dog, Brandy- a named of wine . He’s black and white and very friendly.You should look after he cos he so naughty.That all about my family,it your turn now.Tell me about your family !!

MINE viết hay đấy 

lô mày

Bài làm:

Ta có: \(3x^2+x-1\)

\(=3\left(x^2+\frac{1}{3}x-\frac{1}{3}\right)\)

\(=3\left(x^2+\frac{1}{3}x+\frac{1}{36}\right)-\frac{13}{12}\)

\(=3\left(x+\frac{1}{6}\right)^2-\frac{13}{12}\ge-\frac{13}{12}\left(\forall x\right)\)

Dấu "=" xảy ra khi: \(3\left(x+\frac{1}{6}\right)^2=0\Rightarrow x=-\frac{1}{6}\)

Vậy \(Min=-\frac{13}{12}\Leftrightarrow x=-\frac{1}{6}\)

Ta có: \(A=\frac{1}{1.2}+\frac{1}{3.4}+\frac{1}{5.6}+...+\frac{1}{199.200}\)

\(=1-\frac{1}{2}+\frac{1}{3}-\frac{1}{4}+\frac{1}{5}-\frac{1}{6}+...+\frac{1}{199}-\frac{1}{200}\)

\(=\left(1+\frac{1}{3}+\frac{1}{5}+...+\frac{1}{199}\right)-\left(\frac{1}{2}+\frac{1}{4}+...+\frac{1}{200}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200}\right)-2\left(\frac{1}{2}+\frac{1}{4}+\frac{1}{6}+...+\frac{1}{200}\right)\)

\(=\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{200}\right)-\left(1+\frac{1}{2}+\frac{1}{3}+...+\frac{1}{100}\right)\)

\(=\frac{1}{101}+\frac{1}{102}+\frac{1}{103}+...+\frac{1}{200}\)

\(\Rightarrow A=B\)

Khi đó, \(\frac{A}{B}=1\)

It's khai triển :)

a) \(\left(5x-x^2\right)\left(5x+x^2\right)=25x^2-x^4\)

b) \(\left(2x-y\right)\left(4x^2+2xy+y^2\right)=8x^3-y^3\)

c) \(\left(x+3\right)\left(x^2-3x+9\right)=x^3-27\)

d) \(-x^3+3x^2-3x+1=\left(1-x\right)^3\)

e) \(x^2-2x+9=\left(x-1\right)^2+8??\) ko ra gì cả-.-

g) \(\left(x+1\right)\left(x-1\right)=x^2-1\)

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

i) \(25a^2+4b^2-20ab=\left(5a-2b\right)^2\)

Bài làm:

Ta có: \(2^{15}+4^8+8^6\)

\(=2^{15}+2^{16}+2^{18}\)

\(=2^{15}\left(1+2+2^3\right)\)

\(=2^{15}.11\) \(⋮\) \(11\)

\(=2^{14}.22\) \(⋮\) \(22\)

=> đpcm

vô lí vì khi cắt thì bao giờ diện tích còn lại luôn nhỏ hơn diện tích ban đầu.