Pt có nghiệm: \(\Rightarrow m^2+\left(2m+1\right)^2\ge\left(3m+1\right)^2\)

                       \(\Rightarrow m^2+4m^2+4m+1\ge9m^2+6m+1\)

                       \(\Rightarrow-4m^2-2m\ge0\)

                       \(\Rightarrow-\dfrac{1}{2}\le m\le0\) thì pt có nghiệm.

    \(2cos^2x-5sinx-2=0\)

\(\Rightarrow2\left(1-sin^2x\right)-5sinx-2=0\)

\(\Rightarrow-2sin^2x-5sinx=0\)

\(\Rightarrow\left\{{}\begin{matrix}sinx=0\\2sinx+5=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=k\pi\\sinx=-\dfrac{5}{2}\left(l\right)\end{matrix}\right.\)\(\left(k\in Z\right)\)

a) \(E_P=E_A+E_B=k\cdot\dfrac{\left|q_1\right|}{AP^2}+k\cdot\dfrac{\left|q_2\right|}{BP^2}\)

                            \(=9\cdot10^9\cdot\left(\dfrac{4\cdot10^{-6}}{0,04^2}+\dfrac{1\cdot10^{-6}}{0,04^2}\right)=2,8125\cdot10^7\)V/m

c)    \(sinx+cosx=1\)

   \(\Rightarrow\)\(\sqrt{2}sin\left(x+\dfrac{\pi}{2}\right)=1\) \(\Rightarrow sin\left(x+\dfrac{\pi}{2}\right)=\dfrac{1}{\sqrt{2}}\)\(=sin\dfrac{\pi}{4}\)

   \(\Rightarrow\left\{{}\begin{matrix}x+\dfrac{\pi}{2}=\dfrac{\pi}{4}+k2\pi\\x+\dfrac{\pi}{2}=\pi-\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\)

   \(\Rightarrow\left\{{}\begin{matrix}x=-\dfrac{\pi}{4}+k2\pi\\x=\dfrac{\pi}{4}+k2\pi\end{matrix}\right.\) \(\left(k\in Z\right)\)

\(tan\left(\dfrac{3x}{2}-10^o\right)=-\dfrac{1}{\sqrt{3}}=tan\left(-30^o\right)\)

\(\Rightarrow\dfrac{3x}{2}-10^o=-30^o+k180^o\)

\(\Rightarrow\dfrac{3x}{2}=-20^o+k180^o\)

\(\Rightarrow x=-\dfrac{1}{3}\cdot40^o+k120^o\) \(\left(k\in Z\right)\)

a) cos\(\left(\dfrac{2x}{3}+\dfrac{\pi}{4}\right)\)=\(-\dfrac{1}{2}\)

  \(\Rightarrow cos\left(\dfrac{2x}{3}+\dfrac{\pi}{4}\right)=cos\dfrac{2\pi}{3}\)

  \(\Rightarrow\left\{{}\begin{matrix}\dfrac{2x}{3}+\dfrac{\pi}{4}=\dfrac{2\pi}{3}+k2\pi\\\dfrac{2x}{3}+\dfrac{\pi}{4}=-\dfrac{2\pi}{3}+k2\pi\end{matrix}\right.\)

  \(\Rightarrow\left\{{}\begin{matrix}\dfrac{2x}{3}=\dfrac{5\pi}{12}+k2\pi\\\dfrac{2x}{3}=-\dfrac{11\pi}{12}+k2\pi\end{matrix}\right.\)

  \(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{5\pi}{8}+k3\pi\\x=-\dfrac{11\pi}{8}+k3\pi\end{matrix}\right.\)(\(k\in Z)\)

\(n_{Zn}=\dfrac{16,25}{65}=0,25mol\)

 \(Zn+2HCl\rightarrow ZnCl_2+H_2\)

0,25     0,5          0,25

\(m_{ZnCl_2}=0,25\cdot136=34g\)

\(V_{HCl}=\dfrac{n_{HCl}}{C_{M_{HCl}}}=\dfrac{0,5}{0,2}=2,5l\)