Bài2:

\(Pt\Leftrightarrow\left(3m-2\right)\left(1-\cos2x\right)-\left(10m-4\right)\sin2x+3\left(2m+1\right)\left(1+\cos2x\right)=0.\)

\(\Leftrightarrow\cos2x\left(3m+5\right)-\sin2x\left(10m-4\right)+9m+1=0\)

Pt vô nghệm \(\Leftrightarrow\left(10m-4\right)^2+\left(3m+5\right)^2-\left(9m+1\right)^2< 0\Leftrightarrow28m^2-68m+40< 0\)

\(\Leftrightarrow\frac{10}{7}>m>1\)

Bài 3:

\(pt\Leftrightarrow\cos2x.\cos x+\cos2x-m.\cos^2x-m.\cos x-m.\sin^2x=0\)

\(\Leftrightarrow\cos x.\cos2x+\cos2x-m.\cos x-m=0\Leftrightarrow\left(\cos x+1\right)\left(\cos2x-m\right)=0\Leftrightarrow\orbr{\begin{cases}\cos x=-1\Leftrightarrow x=\left(2k+1\right)\pi\\\cos2x=m\end{cases}}\)Th1: \(x=\left(2k+1\right)\pi\Rightarrow0\le\left(2k+1\right)\pi\le\frac{2\pi}{3}\Leftrightarrow-\frac{1}{2}\le k\le-\frac{1}{6}\Leftrightarrow\)không có k thỏa mãn

=> TH1, pt ko có ngh trên khoảng đã cho

Th2: \(\cos2x=m\)\(x\in\left[0,\frac{\pi}{3}\right]\Rightarrow2x\in\left[0,\frac{2\pi}{3}\right]\)

BBT của hs y=cos2x trên khoảng đã cho:

x 2x y

=> phương trinh có 2 ngh trên khoảng [0,2pi/3] \(\Leftrightarrow-1< m\le-\frac{1}{2}\)

II. Read the short conversations carefully and choose the suitable phrases or expressions in the box to complete the conversations. (5 pts)

A.        Kay: Hi, Sally. (1) _________________________! What are you doing here?

            Sally: Oh, hi, Kay. (2_________________________, I expect…..just shopping.

B.        James: Do you mind if I sit here?

Lucy: No, (3) _____________________. (4) ______________________.

James: I’m James. (5) ______________________________.

Lucy: Hi, I’m Lucy.

C.        Brian: Was everything all right with your meal?

Tracy: (6) ____________________________________.

Brian: (7) _____________________________________

Tracy: No, thanks. Just the bill. We must get back to work.

D.        Peem: Look at the people in that rowing boat. I’m sure they are in trouble.

James: (8) ___________. _____________. Let’s go and get help.

E.         Beggar: Can you spare any change, sir? For the homeless.

Charles: (9) ______________________________.

Diana: Wait a minute. Here you are.

Beggar: Thanks. (10) ____________________________.