1a.
\(\left|1-3x\right|< 5\)
\(\Leftrightarrow\left\{{}\begin{matrix}1-3x>-5\\1-3x< 5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x< 2\\x>-\dfrac{4}{3}\end{matrix}\right.\) \(\Leftrightarrow-\dfrac{4}{3}< x< 2\)
b.
\(A=2sin^2x-1-cosx\left(\sqrt{2}sinx-1\right)\)
\(=\left(\sqrt{2}sinx-1\right)\left(\sqrt{2}sinx+1\right)-cosx\left(\sqrt{2}sinx-1\right)\)
\(=\left(\sqrt{2}sinx-1\right)\left(\sqrt{2}sinx+1-cosx\right)\)
2.
\(\overrightarrow{AB}=\left(3;2\right)\Rightarrow\) đường cao CH nhận (3;2) là 1 vtpt
Phương trình CH:
\(3\left(x-8\right)+2\left(y+11\right)=0\Leftrightarrow3x+2y-2=0\)
b. GỌi G là trọng tâm tam giác \(\Rightarrow G\left(1;-1\right)\)
Phương trình AB:
\(2\left(x+4\right)-3\left(y-3\right)=0\Leftrightarrow2x-3y+17=0\)
\(R=d\left(G;AB\right)=\dfrac{\left|2.1-3\left(-1\right)+17\right|}{\sqrt{2^2+\left(-3\right)^2}}=\dfrac{22}{\sqrt{13}}\)
Phương trình: \(\left(x-1\right)^2+\left(y+1\right)^2=\dfrac{484}{13}\)
