\(a^2+b^2+c^2+ab+bc+ca=0\)

\(\Leftrightarrow2a^2+2b^2+2c^2+2ab+2bc+2ca=0\)

\(\Leftrightarrow a^2+2ab+b^2+b^2+2bc+c^2+c^2+2ca+a^2=0\)

\(\Leftrightarrow\left(a+b\right)^2+\left(b+c\right)^2+\left(c+a\right)^2=0\)

\(\Leftrightarrow\hept{\begin{cases}a+b=0\\b+c=0\\c+a=0\end{cases}}\Leftrightarrow a=b=c=0\)

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

\(\Leftrightarrow\frac{2}{3}x-2-x+\frac{1}{2}=\frac{1}{2}\)

\(\Leftrightarrow\frac{-x}{3}=2\)

\(\Leftrightarrow x=-6\)

giúp mình với mọi người ơi

Ta có 3(a² + b² + c²) = (a + b + c)² 

<=> 3a² + 3b² + 3c² = a² + b² + c² + 2ab + 2bc + 2ca 

<=> 2a² + 2b² + 2c² - 2ab - 2bc - 2ca = 0

<=> (a - b)² + (b - c)² + (c - a)² = 0

<=> \(\hept{\begin{cases}a-b=0\\b-c=0\\c-a=0\end{cases}}\Leftrightarrow a=b=c\)(đpcm)

carm own anh

\(A=\frac{2}{3^2}+\frac{2}{5^2}+\frac{2}{7^2}+...+\frac{2}{2017^2}\)

\(< \frac{2}{3^2-1}+\frac{2}{5^2-1}+\frac{2}{7^2-1}+...+\frac{2}{2017^2-1}\)

\(=\frac{2}{2.4}+\frac{2}{4.6}+\frac{2}{6.8}+...+\frac{2}{2016.2018}\)

\(=\frac{1}{2}-\frac{1}{4}+\frac{1}{4}-\frac{1}{6}+\frac{1}{6}-\frac{1}{8}+...+\frac{1}{2016}-\frac{1}{2018}\)

\(=\frac{1}{2}-\frac{1}{2018}=\frac{504}{1009}\)

\(x\div y=-2\div5\Leftrightarrow\frac{x}{-2}=\frac{y}{5}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có: 

\(\frac{x}{-2}=\frac{y}{5}=\frac{2x+5y}{2.\left(-2\right)+5.5}=\frac{21}{21}=1\)

\(\Leftrightarrow\hept{\begin{cases}x=1.\left(-2\right)=-2\\y=1.5=5\end{cases}}\)

BON=\(90^o\)
tui thử r

mọi người ơi giúp mình với

\(A=0,75+\frac{2}{5}-\left(1+\frac{2}{5}\right)+\frac{5}{4}\)

\(=\frac{3}{4}-1+\frac{5}{4}\)

\(=2-1=1\)