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a, x+7=-12
\(\Leftrightarrow\) x= -19
b, x-15=-21
\(\Leftrightarrow\) x= -6
c, 13-x=20
\(\Leftrightarrow\) x=-7
Bài 2
b)\(\overrightarrow{AN}=\dfrac{1}{2}\left(\overrightarrow{AB}+\overrightarrow{AC}\right)\)
\(\overrightarrow{AK}=\dfrac{1}{2}\left(\overrightarrow{AB}+\overrightarrow{AN}\right)=\dfrac{1}{2}\left(\overrightarrow{AB}+\dfrac{1}{2}\overrightarrow{AB}+\dfrac{1}{2}\overrightarrow{AC}\right)=\dfrac{3}{4}\overrightarrow{AB}+\dfrac{1}{4}\overrightarrow{AC}\)
d)\(S_{ABC}=24\Leftrightarrow\dfrac{1}{2}AN.BC=24\Leftrightarrow AN=6\left(cm\right)\)
\(\left|\overrightarrow{AB}+\overrightarrow{AC}\right|=\left|2.\dfrac{1}{2}\left(\overrightarrow{AB}+\overrightarrow{AC}\right)\right|=\left|2\overrightarrow{AN}\right|=2.AN=12\left(cm\right)\)
Bài 3:
b)\(\overrightarrow{BG}=\overrightarrow{BC}+\overrightarrow{CG}=\overrightarrow{BC}+\dfrac{3}{4}\overrightarrow{CA}=\overrightarrow{BC}+\dfrac{3}{4}\left(\overrightarrow{BA}-\overrightarrow{BC}\right)=\dfrac{1}{4}\overrightarrow{BC}+\dfrac{3}{4}\overrightarrow{BA}=\dfrac{1}{4}\overrightarrow{v}+\dfrac{3}{4}\overrightarrow{u}\)
c)Nhìn hình thấy ko thẳng nên đề sai
a)\(f\left(x+1\right)=x^2-3x+2=\left(x^2+2x+1\right)-5x-5+7=\left(x+1\right)^2-5\left(x+1\right)+7\)
\(\Rightarrow f\left(x\right)=x^2-5x+7\)
b)
\(f\left(x+\frac{1}{x}\right)=x^2+\frac{1}{x^2}=x^2+2+\frac{1}{x^2}-2=\left(x+\frac{1}{x}\right)^2-2\)
\(\Rightarrow\left\{\begin{matrix}!x!\ge2\\f\left(x\right)=x^2-2\end{matrix}\right.\)
c)\(f\left(\frac{1}{x}\right)=x+\sqrt{1+x^2}=\frac{1}{\frac{1}{x}}+\sqrt{1+\frac{1}{\frac{1}{x^2}}}\Rightarrow f\left(x\right)=\frac{1}{x}+\sqrt{1+\frac{1}{x^2}}\left(x\ne0\right)\)