1. I saw your Institute's advertisement on Today's TV program yesterday.

3. I have learnt English for 4 years and want to improve my listening and speaking.

5. I can complete my spoken English test if necessary.

1. False
2. True
3. True
4. True

a) Điều kiện xác định: \(x^2-1\ge0\Leftrightarrow\left[{}\begin{matrix}x\ge1\\x\le-1\end{matrix}\right.\)

\(\sqrt{x^2-1}-x=0\)

\(\Leftrightarrow\sqrt{x^2-1}=x\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\x^2-1=x^2\end{matrix}\right.\)

\(\Leftrightarrow\left\{{}\begin{matrix}x\ge0\\-1=0\end{matrix}\right.\) (vô lí)

\(\Rightarrow\) Phương trình vô nghiệm.

b) Điều kiện xác định: \(4-x\ge0\Leftrightarrow x\le4\)

\(\sqrt{4-x}-2< 0\)

\(\Leftrightarrow\sqrt{4-x}< 2\)

\(\Leftrightarrow0\le4-x< 4\)

\(\Leftrightarrow-4\le-x< 0\)

\(\Leftrightarrow4\ge x>0\)

Vậy \(4\ge x>0\)

Yêu cầu bài toán: \(\sqrt{x}-\sqrt{y}=\sqrt{\dfrac{3}{2}}-\dfrac{\sqrt{2}}{2}\)

Nhận thấy: 

\(\sqrt{2-\sqrt{3}}\)

\(=\sqrt{\dfrac{4-2\sqrt{3}}{2}}\)

\(=\sqrt{\dfrac{\left(\sqrt{3}-1\right)^2}{2}}\)

\(=\dfrac{\left|\sqrt{3}-1\right|}{\sqrt{2}}\)

\(=\dfrac{\sqrt{3}-1}{\sqrt{2}}\) (vì \(\sqrt{3}-1>0\))

\(=\sqrt{\dfrac{3}{2}}-\dfrac{\sqrt{2}}{2}\)

Yêu cầu bài toán \(\Rightarrow\left\{{}\begin{matrix}x=\dfrac{3}{2}\\y=\dfrac{1}{2}\end{matrix}\right.\)

1. Susan and Joe join the school theater group.
2. They are rehearsing a play for the Teacher's Day.
3. Susan and Joe are the members of the stamp collector's club.
4. Jack and Jill play for the school football team.
5. Liam and Thomas are the members of the school art club.

a) \(x\left(5x-3\right)-x^2\left(x-1\right)+x\left(x^2-6x\right)-10+3x\)

\(=5x^2-3x-x^3+x^2+x^3-6x^2-10+3x\)

\(=-10\)

b) \(x\left(x^2+x+1\right)-x^2\left(x+1\right)-x+5\)

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

\(=5\)

   1,       P     +    5HNO₃  -->   H₃PO₄    +    5NO₂    +  H₂O

2,     MnO₂   +     4HCl -->     MnCl₂   +    Cl₂    +   2H₂O

3,       2FeO  +  4H₂SO₄   --> Fe₂(SO₄)₃   +    SO₂     +  4H₂O

4,       2Fe₃O₄ +  10H₂SO₄đặc nóng     --> 3Fe₂(SO₄)₃   +    SO₂     +  10H₂O

5,     Fe   +    6HNO₃ đặc nóng  -->   Fe(NO₃)₃      +    3NO₂    +  3H₂O

6,     4Fe   +    10HNO₃ loãng nguội -->   4Fe(NO₃)₂     +    N₂O    +  5H₂O

It used to take him forty minutes to do the test 

He used to spend forty minutes doing the test.

Theo giả thiết, ta có: \(x+y=-3\)

\(\Rightarrow\left(x+y\right)^2=\left(-3\right)^2\)

\(x^2+2xy+y^2=9\)

\(x^2+y^2=9-2xy\)

\(x^2+y^2=9+2.10\)

\(x^2+y^2=29\)

Do đó:

\(x^3+y^3\)

\(=\left(x+y\right)\left(x^2-xy+y^2\right)\)

\(=\left(x+y\right)\left[\left(x^2+y^2\right)-xy\right]\)

\(=-3\left[29+10\right]\)

\(=-3.39\)

\(=-117\)