Bổ sung câu a:

Với y = 2, ta có: ...

Với y = 3, ta có: 

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

Vậy phương trình có nghiệm là: (x;y) = (-1;-2), (2;-2), (-2;-1), (3;-1), (-2;2), (3;2), (-1;3), (2;3).

a. Phương trình <=> 4x² + 4y² - 4x - 4y = 32 <=> (4x² - 4x + 1) + (4y² - 4y + 1) = 34 <=> (2x - 1)² + (2y - 1)² = 34

Vì (2x - 1)² \(\ge\) 0 => (2y - 1)² \(\le\) 34 => \(-\sqrt{34}\le\) 2y - 1 \(\le\sqrt{34}\) <=> \(1-\sqrt{34}\le2y\le1+\sqrt{34}\Leftrightarrow\dfrac{1-\sqrt{34}}{2}\le y\le\dfrac{1+\sqrt{34}}{2}\)

Mà y nguyên nên \(y\in\left\{-2;-1;0;1;2;3\right\}.\)

Với \(y=-2,\) ta có:

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

Với \(y=-1,\) ta có:

\(x^2-x-6=0\Leftrightarrow\left(x^2-3x\right)+\left(2x-6\right)=0\Leftrightarrow x\left(x-3\right)+2\left(x-3\right)=0\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\Leftrightarrow x=-2\) (nhận) hoặc \(x=3\) (nhận)

Với \(y=0,\) ta có: \(x^2-x-8=0.\) Phương trình này không có nghiệm nguyên.

Với \(y=1,\) ta có: \(x^2-x-8=0.\) Phương trình này không có nghiệm nguyên.

Với \(y=2,\) ta có:

\(x^2-x-6=0\Leftrightarrow\left(x^2-3x\right)+\left(2x-6\right)=0\Leftrightarrow x\left(x-3\right)+2\left(x-3\right)=0\Leftrightarrow\left(x+2\right)\left(x-3\right)=0\Leftrightarrow x=-2\) (nhận) hoặc \(x=3\) (nhận)

Vậy phương trình có nghiệm là: \(\left(x;y\right)=\left(-1;-2\right),\left(2;-2\right),\left(-2;-1\right),\left(3;-1\right),\left(-2;2\right),\left(3;2\right).\)

b. Phương trình <=> (4x² - 4x + 1) + (y² + x² + 4 - 2xy + 4x - 4y) = 5 <=> (2x - 1)² + (y - x - 2)² = 5

Vì (y - x - 2)² \(\ge0\Rightarrow\left(2x-1\right)^2\le5\Leftrightarrow-\sqrt{5}\le2x-1\le\sqrt{5}\Leftrightarrow1-\sqrt{5}\le2x\le1+\sqrt{5}\Leftrightarrow\dfrac{1-\sqrt{5}}{2}\le x\le\dfrac{1+\sqrt{5}}{2}\)

Mà x nguyên nên \(x\in\left\{0;1\right\}.\)

Với \(x=0,\) ta có: \(y^2-4y=0\Leftrightarrow y\left(y-4\right)=0\Leftrightarrow y=0\) (nhận) hoặc \(y=4\) (nhận)

Với \(x=1,\) ta có: 

\(y^2-6y+5=0\Leftrightarrow\left(y^2-5y\right)-\left(y-5\right)=0\Leftrightarrow y\left(y-5\right)-\left(y-5\right)=0\Leftrightarrow\left(y-1\right)\left(y-5\right)=0\Leftrightarrow y=1\) (nhận) hoặc \(y=5\) (nhận)

Vậy phương trình có nghiệm là: \(\left(x;y\right)=\left(0;0\right),\left(0;4\right),\left(1;1\right),\left(1;5\right).\)

1. c. of

2. b. for

3. b. less

4. a. its

5. c. density

6. d. don't they

7. b. Though

8. d. affecting

9. c. won't we

10. b. No doubt

1.     We didn’t go for a walk ______________it was too cold. ( because/ because of)

2.     Nam failed the exam _____________he was lazy ( because/ because of)

3.     She couldn’t unlock it ______________ she had a wrong key. ( because of/ because)

4.     Julie passed the exam ______________ working very hard. ( because/ because of)

5.     He had an accident _______________ his carelessness. ( because/ because of)

6.     The boy can’t reach the bookshelf ____________he is not tall enough. ( because/ because of)

7.     They decided not to go out for  a meal ___________ being too tired. ( because of/ because)

8.     I want to learn English _____________ I want to get a better job. ( because of/ because)

9.     We watched TV the whole evening __________ we had nothing to do ( because/ because of)

10.___________ the heavy rain, we cancelled out trip. ( Because / Because of)

11._______not wearing the hat, she had a headache. ( Because of/ Because)

12. ___________only a little milk, I can’t make cakes. ( Because / Because of)

13._________ I didn’t do the homework carefully, the teacher punished me. ( Because of/ Because)

14._________ the expensive dictionary, I couldn’t buy it. ( Because of/ Because)

15. I couldn’t see my uncle ____________ I was late. ( Because / Because of)

\(\left[\dfrac{1}{3}\left(\dfrac{6}{5}-\dfrac{9}{4}\right)-\dfrac{7}{5}\left(\dfrac{15}{14}+\dfrac{5}{7}\right)\right]:\left(\dfrac{1}{2}-\dfrac{1}{3}+\dfrac{5}{6}\right)\)

\(=\left[\dfrac{1}{3}.\dfrac{6}{5}-\dfrac{1}{3}.\dfrac{9}{4}-\dfrac{7}{5}.\dfrac{15}{14}-\dfrac{7}{5}.\dfrac{5}{7}\right]:\left(\dfrac{3}{2.3}-\dfrac{2}{3.2}+\dfrac{5}{6}\right)\)

\(=\left[\dfrac{2}{5}-\dfrac{3}{4}-\dfrac{3}{2}-1\right]:\left(\dfrac{3}{6}-\dfrac{2}{6}+\dfrac{5}{6}\right)\)

\(=\left[\dfrac{2.4}{5.4}-\dfrac{3.5}{4.5}-\dfrac{3.10}{2.10}-\dfrac{20}{20}\right]:1\)

\(=\dfrac{8}{20}-\dfrac{15}{20}-\dfrac{30}{20}-\dfrac{20}{20}\)

\(=-\dfrac{57}{20}\)

\(\dfrac{6}{13}-\dfrac{2}{5}+\dfrac{7}{13}+\dfrac{8}{5}-\dfrac{1}{5}\)

\(=\left(\dfrac{6}{13}+\dfrac{7}{13}\right)+\left(\dfrac{8}{5}-\dfrac{1}{5}-\dfrac{2}{5}\right)\)

\(=\dfrac{13}{13}+\dfrac{5}{5}\)

\(=1+1\)

\(=2\)

x² - 2xy + y² + 3x - 3y - 4

= (x² - 2xy + y²) + (3x - 3y) - 4

= (x - y)²​ + 3(x - y) - 4

= [(x - y)²​ - (x - y)] + [4(x - y) - 4]

= (x - y)(x - y - 1) + 4(x - y - 1)

= (x - y + 4)(x - y - 1)

1. I hope I will come to England next year and spend some months in London.

2. Who is responsible for all the noise at last?

3. The driver stops his car in time to save a child.

4. If there is fine weather, I will have an excursion to Vung Tau tomorrow.

5. He closes the door so mosquitoes are not in.

6. It is difficult to get in touch with the manager in that company.

7. The wind blows out violently so that all the trees are uprooted.

8. Nobody can predict what happened.

9. I stay in all Sunday to do mathematics problems.

10. It is untrue that all televison programs are good for children.

B3

a) x³ + x²y - 4x - 4y

= (x³ + x²y) - (4x + 4y)

= x²(x + y) - 4(x + y)

= (x²​ - 4)(x + y)

= (x​ - 2)(x + 2)(x + y)

b) x³ - 4x² + 4x - 1

= (x³ - 1) - (4x² - 4x)

= (x - 1)(x² + x + 1) - 4x(x - 1)

= (x - 1)(x² + x + 1 - 4x) 

= (x - 1)(x² - 3x + 1) 

c) x⁴ - x³y - x + y

= (x⁴ - x³y) - (x - y)

= x³(x - y) - (x - y)

= (x³ - 1)(x - y)

= (x - 1)(x² + x + 1)(x - y)

1. a. in
2. b. used to
3. b. to move
4. d. b & c
5. a. pollution
6. a. Because