\(3.\)

\(a,\)

\(\left(2x-3\right)^2-\left(x+5\right)^2=0\)

\(\Leftrightarrow4x^2-12x+9-x^2-10x-25=0\)

\(\Leftrightarrow3x^2-22x-16=0\)

\(\Leftrightarrow3.\left(x-8\right)\left(x+\dfrac{2}{3}\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}3=0\left(\text{vô lí}\right)\\x-8=0\\x+\dfrac{2}{3}=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=-\dfrac{2}{3}\end{matrix}\right.\)

Vậy \(S=\left\{8;-\dfrac{2}{3}\right\}\)

\(b,\)

\(\left(x^3-x^2\right)-4x^2+8x-4=0\)

\(\Leftrightarrow x^3-5x^2+8x-4=0\)

\(\Leftrightarrow\left(x-1\right)\left(x-2\right)^2=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-1=0\\\left(x-2\right)^2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x-2=0\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=2\end{matrix}\right.\)

Vậy \(S=\left\{1;2\right\}\)

\(4.\)

\(a,\)

\(16x^3y+\dfrac{1}{4}yz^3\)

\(=\dfrac{1}{4}y\left(64x^3+z^3\right)\)

\(=\dfrac{1}{4}y\left(4x+z\right)\left(16x^2-4xz+z^2\right)\)

\(b,\)

\(x^{m+4}-x^{m+3}-x-1\)

\(=x^m.x^4-x^m.x^3-x-1\)

\(=x^m.\left(x^4-x^3\right)-x-1\)

\(=x^m.x^3.\left(x+1\right)-\left(x+1\right)\)

\(=\left(x^{m+3}-1\right)\left(x+1\right)\)

\(-3x\left(x-2\right)+5x^4-x^2\left(x-3\right)-6x+2\)

\(=-3x^2+6x+5x^4-x^3+3x^2-6x+2\)

\(=5x^4+\left(-x^3\right)+\left(-3x^2+3x^2\right)+\left(6x-6x\right)+2\)

\(=5x^4-x^3+2\)

Xét \(\triangle ABE\) và \(\triangle HBE\):

\(BE\) chung

\(\widehat{BAE}=\widehat{BHE}=90^o\)

\(\widehat{ABE}=\widehat{HBE}\) 

\(\Rightarrow\Delta ABE=\Delta HBE\left(ch-gn\right)\).

\(a,\)

Xét \(\triangle ADC\) và \(\triangle MDB\):

\(DA=DM\)

\(DC=DB\)

\(\widehat{ADC}=\widehat{MDB}\) 

\(\Rightarrow\Delta ADC=\Delta MDB\left(c.g.c\right)\) \(\left(1\right)\)

\(\left(1\right)\Rightarrow AC=BM\)

\(\Rightarrow\widehat{ACD}=\widehat{MBD}\)

mà hai góc này nằm ở vị trí so le trong

\(\Rightarrow\)\(AC//BM\)

\(b,\)

\(\left(1\right)\Rightarrow\widehat{DAC}=\widehat{DMB}\)

Xét \(\triangle ABM\) và \(\triangle MCA\):

\(AM\) chung

\(BM=AC\)

\(\widehat{DAC}=\widehat{DMB}\)

\(\Rightarrow\Delta ABM=\Delta MCA\left(c.g.c\right)\).

1. A: What were you doing (you, do) when the accident occurred?

    B: I was trying (try) to change a light bulb that had burnt out.

2. Sandy is in the living room watching television. At this time yesterday, she was also watching (watch, also) television.

3. A: I called (call) you last night after dinner, but you weren't (be, not) there. Where were you?

    B: I was working (work) out at the fitness center.

4. When I walked (walk) into the busy office, the secretary was talking (talk) on the phone with a custtomer, several clerks were working busily (work, busily) at their desks, and two managers were discussing (discuss, quietly) methods to improve customer service.

5. I was watching (watch) a mystery movie on TV when the electricity went out. Now I am never going to find out how the movie ands.

6. The Titanic was crossing (cross) the Atlantic when it struck (strike) an iceberg.

1. The couple decided to separate after years of arguing.

2. The thief tried to enter the house through the back door.

3. My car broke down on the way to work, so I had to call for a tow truck.

4. The prisoners managed to escape of the jail using a secret tunnel.

5. They decided to end their engagement due to irreconcilable differences.

6. C

7. B

8. D

1. closing

2. in

3. for

4. in

5. reading

6. yet

7. in oder to 

8. closing

9. to pass

10. talking

1. Hoa is better than any other student in the class.

2. Phu Quoc is bigger than any other island in Vietnam.

3. My house is the most modern house in the village.

4. Ba is the most intelligent person in the group.

5. Ho Chi Minh City is the biggest city in Vietnam.

6. Australia is the most popular country in the world.

1. A

2. A

3. B

4. A

5. B

6. B

7. A