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17 tháng 12 2023

m: \(\left(-7x+7\right)\left(2x+100\right)=0\)

=>\(\left[{}\begin{matrix}-7x+7=0\\2x+100=0\end{matrix}\right.\)

=>\(\left[{}\begin{matrix}-7x=-7\\2x=-100\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-50\end{matrix}\right.\)

n: \(2x\left(x+2023\right)\left(-4x+8\right)=0\)

=>\(2\cdot x\left(x+2023\right)\cdot\left(-4\right)\left(x-2\right)=0\)
=>x(x-2)(x+2023)=0

=>\(\left[{}\begin{matrix}x=0\\x-2=0\\x+2023=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=2\\x=-2023\end{matrix}\right.\)

o: \(-2024x\left(4x-4\right)\left(-2x+6\right)=0\)

=>\(x\left(4x-4\right)\left(-2x+6\right)=0\)

=>\(x\cdot4\left(x-1\right)\cdot\left(-2\right)\left(x-3\right)=0\)

=>x(x-1)(x-3)=0

=>\(\left[{}\begin{matrix}x=0\\x-1=0\\x-3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=3\end{matrix}\right.\)

p: -17-2x=199

=>2x=-17-199=-216

=>x=-216/2=-108

q: -24+2x=100

=>2x=100+24=124

=>\(x=\dfrac{124}{2}=62\)

r: \(119-\left(x+5\right)=-21\)

=>\(x+5=119-\left(-21\right)=119+21=140\)

=>x=140-5=135

s: \(-24+\left(-7+x\right)=45\)

=>\(\left(x-7\right)-24=45\)

=>x-31=45

=>x=45+31=76

t: \(-146-\left(-5+x\right)=-6\)

=>\(x-5=-146-\left(-6\right)=-140\)

=>x=-140+5=-135

u: \(-29+4\left(1-5x\right)=-45\)

=>4(1-5x)=-45+29=-16

=>1-5x=-4

=>5x=1+4=5

=>\(x=\dfrac{5}{5}=1\)

v: \(24-5\left(-3+2x\right)=59\)

=>\(24-5\left(2x-3\right)=59\)

=>5(2x-3)=24-59=-35

=>2x-3=-7

=>2x=-4

=>x=-4/2=-2

17 tháng 12 2023

-17-2x=199

<=>-2x=216

<=>x=-108

 

-24+2x=100

<=>2x=124

<=>x=62

 

-24+(-7+x)=45

<=>-7+x=69

<=>x=76

 

-146-(-5+x)=-6

<=>-146+5-x=-6

<=>x=-135

 

-29+4(1-5x)=-45

<=>-29+4+20x=-45

<=>20x=-20

<=>x=-1

 

24-5(-3+2x)=59

<=>24+15-10x=59

<=>-10x=20

<=>x=-2

14 tháng 8 2021

1 A

2 B

3 B

4 D

5 C

6 D

7 C

8 C

9 A

10 D

11 C

12 B

13 D

14 A

15 A

16 B

28 tháng 10 2021

2. D

3. A 

NV
23 tháng 10 2021

\(2\left(\overrightarrow{IA}+\overrightarrow{AB}\right)+3\left(\overrightarrow{IA}+\overrightarrow{AC}\right)=\overrightarrow{0}\Leftrightarrow5\overrightarrow{IA}+2\overrightarrow{AB}+3\overrightarrow{AC}=\overrightarrow{0}\)

\(\Leftrightarrow\overrightarrow{AI}=\dfrac{2}{5}\overrightarrow{AB}+\dfrac{3}{5}\overrightarrow{AC}\)

\(\overrightarrow{JB}+\overrightarrow{BA}+3\overrightarrow{JB}+3\overrightarrow{BC}=\overrightarrow{0}\Leftrightarrow\overrightarrow{BJ}=-\dfrac{1}{4}\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{BC}=-\dfrac{1}{4}\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{BA}+\dfrac{3}{4}\overrightarrow{AC}\)

\(=-\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{AC}\)

\(\Rightarrow\overrightarrow{AI}.\overrightarrow{BJ}=\left(\dfrac{2}{5}\overrightarrow{AB}+\dfrac{3}{5}\overrightarrow{AC}\right)\left(-\overrightarrow{AB}+\dfrac{3}{4}\overrightarrow{AC}\right)\)

\(=-\dfrac{2}{5}AB^2+\dfrac{9}{20}AC^2-\dfrac{3}{10}\overrightarrow{AB}.\overrightarrow{AC}\)

\(=-\dfrac{3}{5}a^2+\dfrac{9}{20}a^2-\dfrac{3}{10}a^2.cos60^0=-\dfrac{3}{10}a^2\)

NV
23 tháng 10 2021

b.

Từ câu a ta có

\(\overrightarrow{AI}=\dfrac{2}{5}\overrightarrow{AB}+\dfrac{3}{5}\overrightarrow{AC}\) (1)

\(\overrightarrow{JA}+3\overrightarrow{JC}=\overrightarrow{0}\Leftrightarrow\overrightarrow{JA}+3\overrightarrow{JA}+3\overrightarrow{AC}=\overrightarrow{0}\Leftrightarrow\overrightarrow{JA}=-\dfrac{3}{4}\overrightarrow{AC}\) (2)

Cộng vế (1) và (2):

\(\overrightarrow{JA}+\overrightarrow{AI}=-\dfrac{3}{4}\overrightarrow{AC}+\dfrac{2}{5}\overrightarrow{AB}+\dfrac{3}{5}\overrightarrow{AC}\)

\(\Leftrightarrow\overrightarrow{JI}=\dfrac{2}{5}\overrightarrow{AB}-\dfrac{3}{20}\overrightarrow{AC}\)

\(\Rightarrow IJ^2=\overrightarrow{JI}^2=\left(\dfrac{3}{5}\overrightarrow{AB}-\dfrac{3}{20}\overrightarrow{AC}\right)^2=\dfrac{9}{25}AB^2+\dfrac{9}{400}AC^2-\dfrac{9}{50}\overrightarrow{AB}.\overrightarrow{AC}\)

\(=\dfrac{9}{25}a^2+\dfrac{9}{400}a^2-\dfrac{9}{50}.a^2.cos60^0=...\)