a) \(x^2-3x+3=0\)

\(\Leftrightarrow x^2-2.x.\frac{3}{2}+\left(\frac{3}{2}\right)^2+\frac{3}{4}=0\)

\(\Leftrightarrow\left(x-\frac{3}{2}\right)^2+\frac{3}{4}=0\)

\(\Leftrightarrow\left(x-\frac{3}{2}\right)^2=\frac{-3}{4}\)

Vô lí => Phương trình vô nghiệm

\(\Rightarrow x\in\varnothing\)

b) \(x-\left(x-2\right)-\left(x-2\right)=0\)

\(\Leftrightarrow x-x+2-x+2=0\)

\(\Leftrightarrow-x=-4\)

\(\Leftrightarrow x=4\)

c) \(\left(x-2\right)\left(x-1\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-2=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=2\\x=1\end{cases}}}\)

Vậy x = {1;2} 

d) \(x^2-2x-x+2=0\)

\(\Leftrightarrow x\left(x-1\right)-2\left(x-1\right)=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x-1=0\\x-2=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=1\\x=2\end{cases}}}\)

Vậy x = {1;2}

ta có : \(\frac{x}{7}=\frac{y}{13}\)

ADTCDTSBN : 

\(\frac{x}{7}=\frac{y}{13}=\frac{x+y}{7+13}=\frac{40}{20}=2\)

\(\Rightarrow\frac{x}{7}=2\Rightarrow x=14\)

\(\frac{y}{13}=2\Leftrightarrow y=26\)

KL : ... 

kb nhoa 

Viết sai chữ Thanks kìa

\(A=\frac{2!+\sqrt{3}}{2!}+\frac{3!+\sqrt{4}}{3!}+\frac{4!+\sqrt{5}}{4!}+....+\frac{2012!+\sqrt{2013}}{2012!}\)

\(=\frac{2!}{2!}+\frac{\sqrt{3}}{2!}+\frac{3!}{3!}+\frac{\sqrt{4}}{3!}+.....+\frac{2012!}{2012!}+\frac{\sqrt{2013}}{2012!}\)

\(=2012+\left(\frac{\sqrt{3}}{2!}+\frac{\sqrt{4}}{3!}+....+\frac{\sqrt{2011}}{2012!}\right)\)

Mà \(\frac{\sqrt{3}}{2!}+\frac{\sqrt{4}}{3!}+...+\frac{\sqrt{2013}}{2012!}>0\)

\(\Rightarrow A>2012+0=2012\)

Đề sai nên t sửa lại r nhé

haizzzz đệ lm sai rồi kìa =((

Do \(b^2=ac;c^2=bd\)

\(\Rightarrow\frac{a}{b}=\frac{b}{c};\frac{b}{c}=\frac{c}{d}\)

\(\Rightarrow\frac{a}{b}=\frac{b}{c}=\frac{c}{d}\)

\(\Rightarrow\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\frac{a}{b}\cdot\frac{b}{c}\cdot\frac{c}{d}=\frac{a}{d}\)

Áp dụng tính chất dãy tỉ số bằng nhau,ta được:

\(\frac{a^3}{b^3}=\frac{b^3}{c^3}=\frac{c^3}{d^3}=\frac{a}{d}=\frac{a^3+b^3+c^3}{b^3+c^3+d^3}\left(đpcm\right)\)