Đặt \(N=\left|a+1\right|-\left|a+2\right|+\left|-2\right|\)

Ta có \(N=\left|a+1\right|-\left|a+2\right|+2\)

Xét các trường hợp :

TH1. Nếu \(a\ge-1\) thì \(N=\left(a+1\right)-\left(a+2\right)+2=1\)

TH2. Nếu \(a\le-2\) thì \(N=-\left(a+1\right)-\left[-\left(a+2\right)\right]+2=3\)

TH3. Nếu \(-2< a< -1\) thì \(N=-\left(a+1\right)-\left(a+2\right)+2=-2a-1\)

Vậy : \(a\le-2\) : N = 3

-2 < a < -1 : N = -2a-1

\(a\ge-1\) : N = 1

Ta luôn có : \(\left|x\right|\ge0\)

Suy ra \(\left|\left|x\right|+15\right|-3\ge\left|0+15\right|-3=12\)

Vậy A đạt giá trị nhỏ nhất bằng 12 tại x = 0

1 '' What kind of sports do you like best?'' asked Peter

=> Peter asked what kind of sports I liked best.

2. '' Are you interested in acting?'' said Linda

=> Linda asked if I was interested in acting.

3. '' Do you like to join our Drama Group?'' asked Linda

=> Linda asked if I liked to join their Drama Group.

4. '' Do you think of the canteen coffee?'' asked Ann

=> Ann asked if I thinked of the canteen coffee.

5. '' What sort drinks do you like?'' said Bill

=> Bill asked what sort drinks I liked.

6. '' What's the name of the college?''

I asked what was the name of the college.

Đặt \(m=\sqrt{x}\), \(n=\sqrt{x+3}\) suy ra \(\left\{\begin{matrix}y=m+n\\n^2-m^2=3\end{matrix}\right.\)

\(\Rightarrow y.\left(n-m\right)=3\) hay \(y.\left(\sqrt{x+3}-\sqrt{x}\right)=3\)

Vậy tới đây bạn đưa về dạng quen thuộc :)

ĐKXĐ : \(-2\le x\le6\)

Xét vế trái : \(VT^2=\left(\sqrt{6-x}+\sqrt{x+2}\right)^2\le2.\left(6-x+x+2\right)=16\)

\(\Rightarrow VT\le4\)

Xét vế phải : \(VP=\left(x^2-6x+9\right)+4=\left(x-3\right)^2+4\ge4\)

Vậy để đẳng thức xảy ra khi VT = VP = 4 => x = 3 (TM)

Ta có :

\(\frac{a}{ab+a+1}+\frac{b}{bc+b+1}+\frac{c}{ac+c+1}=\frac{abc}{ab^2c+abc+bc}+\frac{b}{bc+b+1}+\frac{bc}{abc+bc+b}\)

\(=\frac{1}{bc+b+1}+\frac{b}{bc+b+1}+\frac{bc}{bc+b+1}\)

\(=\frac{bc+b+1}{bc+b+1}=1\) (đpcm)

1. My uncle(not/be) has not been out of his house since he(buy) bought a color TV

2. I don't think I(go) will go out tonight. I (be) am too tired .

3. John(wash) is washing his hands. He(just/repair) has just repaired the TV set.

4. Tell him(bring) to bring his bike inside. If he(leave) leaves it there, someone (steal) will steal it

1. My uncle(not/be) has not been out of his house since he(buy) bought a color TV

2. I don't think I(go) will go out tonight. I (be) am too tired .

3. John(wash) is washing his hands. He(just/repair) has just repaired the TV set.

4. Tell him(bring) to bring his bike inside. If he(leave) leaves it there, someone (steal) will steal it

1. My uncle(not/be) has not been out of his house since he(buy) bought a color TV

2. I don't think I(go) will go out tonight. I (be) am too tired .

3. John(wash) is washing his hands. He(just/repair) has just repaired the TV set.

4. Tell him(bring) to bring his bike inside. If he(leave) leaves it there, someone (steal) will steal it