Chọn D

C

Câu 1:
TXĐ:D=R

\(f\left(-x\right)=2\cdot\left(-x\right)^4-3\cdot\left(-x\right)^2+1\)

\(=2x^4-3x^2+1=f\left(x\right)\)

=>f(x) là hàm số chẵn

\(|2x^2-3x+4|-|2x-x^2-1|=0\)

\(\Leftrightarrow|2x^2-3x+4|=|2x-x^2-1|\)

\(\Leftrightarrow\orbr{\begin{cases}2x^2-3x+4=2x-x^2-1\\2x^2-3x+4=-2x+x^2+1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}2x^2-3x+4-2x+x^2+1=0\\2x^2-3x+4+2x-x^2-1=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x^2-5x+5=0\\x^2-x+3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3\left(x^2-\frac{5}{3}x+\frac{25}{9}-\frac{25}{9}+\frac{5}{3}\right)=0\\x^2-2.x.\frac{1}{2}+\frac{1}{4}-\frac{1}{4}+3=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3\left(x-\frac{5}{3}^2\right)-\frac{10}{3}=0\\\left(x-\frac{1}{2}\right)^2+\frac{11}{4}>0\left(Loai\right)\end{cases}}\)

\(\Leftrightarrow\left(x\sqrt{3}-\frac{5\sqrt{3}}{3}\right)^2-\left(\frac{\sqrt{30}}{3}\right)^2=0\)

\(\Leftrightarrow\left(x\sqrt{3}-\frac{5\sqrt{3}}{3}-\frac{\sqrt{30}}{3}\right)\left(x\sqrt{3}-\frac{5\sqrt{3}}{3}+\frac{\sqrt{30}}{3}\right)=0\)

\(\Leftrightarrow\left(x\sqrt{3}-\frac{\sqrt{30}+5\sqrt{3}}{3}\right)\left(x\sqrt{3}+\frac{\sqrt{30}-5\sqrt{3}}{3}\right)=0\)

\(\Leftrightarrow\orbr{\begin{cases}x\sqrt{3}-\frac{\sqrt{30}+5\sqrt{3}}{3}=0\\x\sqrt{3}+\frac{\sqrt{30}-5\sqrt{3}}{3}=0\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}x=\frac{5+\sqrt{10}}{3}\\x=\frac{5-\sqrt{10}}{3}\end{cases}}\)

Vậy ...

\(\left|2x^2-3x+4\right|-\left|2x-x^2-1\right|=0\)

\(\Leftrightarrow\left|2x^2-3x+4\right|=\left|2x-x^2-1\right|\)

\(\Leftrightarrow\orbr{\begin{cases}2x^2-3x+4=2x-x^2-1\\2x^2-3x+4=x^2-2x+1\end{cases}}\)

\(\Leftrightarrow\orbr{\begin{cases}3x^2-5x+5=0\\x^2-x+3=0\end{cases}}\)

\(TH1:3x^2-5x+5=0\)

Ta có: \(\Delta=5^2-4.3.5=-35< 0\)(vô nghiệm)

\(TH2:x^2-x+3=0\)

Ta có: \(\Delta=1^2-4.1.3=-11< 0\)(vô nghiệm)

Vậy pt vô nghiệm

Câu 9: B

Câu 10: A

Câu 1: C

Câu 2: A

Gọi G là trọng tâm tam giác ABC

\(\Rightarrow T=\sum\left(\overrightarrow{MG}+\overrightarrow{GA}\right)^2=3MG^2+GA^2+GB^2+GC^2+2\overrightarrow{MG}\cdot\left(\overrightarrow{GA}+\overrightarrow{GB}+\overrightarrow{GC}\right)=3MG^2+\dfrac{4}{9}\cdot\left(m_a^2+m_b^2+m_c^2\right)=3MG^2+\dfrac{4}{9}\cdot\left(\dfrac{2b^2+2c^2-a^2}{4}+\dfrac{2a^2+2c^2-b^2}{4}+\dfrac{2b^2+2a^2-c^2}{4}\right)\) = \(3MG^2+\dfrac{1}{3}\left(a^2+b^2+c^2\right)\ge\dfrac{1}{3}\left(a^2+b^2+c^2\right)\) Dấu = xảy ra \(\Leftrightarrow M\equiv G\)

b) \(\dfrac{3\pi}{2}< \alpha< 2\pi\)\(\Rightarrow cos\alpha>0;sin\alpha< 0\)

Có \(1+tan^2\alpha=\dfrac{1}{cos^2\alpha}\)\(\Rightarrow cos\alpha=\dfrac{4}{5}\)

\(sin\alpha=-\sqrt{1-cos^2\alpha}=-\dfrac{3}{5}\)

\(sin\left(\alpha-\dfrac{\pi}{4}\right)=\dfrac{\sqrt{2}}{2}\left(sin\alpha-cos\alpha\right)=\dfrac{\sqrt{2}}{2}\left(-\dfrac{3}{5}-\dfrac{4}{5}\right)=-\dfrac{7\sqrt{2}}{10}\)

Bài 2:

a) Gọi đt d vuông góc với đường thẳng \(\Delta\)có dạng: \(d:-4x+3y+c=0\)

\(A\in\left(d\right)\Rightarrow-4+3+c=0\Leftrightarrow c=1\)

Vậy \(d:-4x+3y+1=0\)

b) Gọi pt đường tròn (C) tâm A có dạng \(\left(C\right):\left(x-1\right)^2+\left(y-1\right)^2=R^2\)

Vì (C) tiếp xúc với \(\Delta\)

\(\Rightarrow\)\(R=d_{\left(A;\Delta\right)}=\dfrac{\left|3+4+5\right|}{\sqrt{3^2+4^2}}=\dfrac{12}{5}\)

\(\Rightarrow\left(C\right):\left(x-1\right)^2+\left(y-1\right)^2=\dfrac{144}{25}\)

Vậy...

CHọn B

B