ta có:

x^2+2x+1= x^2+x+x+1 = (x^2+x)+(x+1) = x*(x+1)+(x+1) = (x+1)*(x+1) = (x+1)^2

Answer:

\(\frac{4x-3y}{5}=\frac{5y-4z}{3}=\frac{3z-5x}{4}\)

\(\Rightarrow\frac{20x-15y}{25}=\frac{15y-12z}{9}=\frac{12z-20x}{16}=\frac{20x-15y+15y-12z+12z-20x}{25+9+16}=0\)

\(\Rightarrow\hept{\begin{cases}\frac{4x-3y}{5}=0\\\frac{5y-4z}{3}=0\\\frac{3z-5x}{4}=0\end{cases}}\Rightarrow\hept{\begin{cases}4x-3y=0\\5y-4z=0\\3z-5x=0\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x}{3}=\frac{y}{4}\\\frac{y}{4}=\frac{z}{5}\\\frac{z}{5}=\frac{x}{3}\end{cases}}\Rightarrow\frac{x}{3}=\frac{y}{4}=\frac{z}{5}=\frac{x-y+z}{3-4+5}=505\)

\(\Rightarrow\hept{\begin{cases}x=505.3=1515\\y=505.4=2020\\z=505.5=2525\end{cases}}\)

CHiều dài mảnh vườn là: 

\(18\times2=36\left(m\right)\)

Chu vi mảnh vườn là: 

\(\left(36+18\right)\times2=108\left(m\right)\)

Phải trồng hết số cây là: 

\(108\div3=36\)(cây) 

Answer:

\(\frac{5x-2}{3}=\frac{-3}{4}\)

\(\Rightarrow20x-8=-9\)

\(\Rightarrow20x=-1\)

\(\Rightarrow x=\frac{-1}{20}\)

\(\left(x^2-\frac{1}{4}\right).\left(x+\frac{2}{5}\right)=0\)

\(\Rightarrow\left(x-\frac{1}{2}\right).\left(x+\frac{1}{2}\right).\left(x+\frac{2}{5}\right)=0\)

Trường hợp 1: \(x-\frac{1}{2}=0\Rightarrow x=\frac{1}{2}\)

Trường hợp 2: \(x+\frac{1}{2}=0\Rightarrow x=\frac{-1}{2}\)

Trường hợp 3: \(x+\frac{2}{5}=0\Rightarrow x=\frac{-2}{5}\)