\(A=-x^2+6x-15\)

\(A=-x^2+2.3x-9-6\)

\(\Rightarrow-A=x^2-2.3x+9+6\)

\(-A=\left(x^2-2.3.x+3^2\right)+6\)

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

\(\Rightarrow A=-\left(x-3\right)^2-6\)

Ta có: \(\left(x-3\right)^2\ge0\forall x\)

\(\Rightarrow-\left(x-3\right)^2\le0\forall x\)

\(\Rightarrow-\left(x-3\right)^2-6\le-6\forall x\)

\(A=-6\Leftrightarrow-\left(x-3\right)^2=0\Leftrightarrow\left(x-3\right)^2=0\Leftrightarrow x-3=0\Leftrightarrow x=3\)

Vậy A_max =-6\(\Leftrightarrow\)x=3

\(B=-2x^2+8x-15\)

\(-2B=4x^2-16x+30\)

\(-2B=\left[\left(2x\right)^2-2.2x.4+4^2\right]+14\)

\(-2B=\left(2x-4\right)^2+14\)

\(\Rightarrow B=-\frac{\left(2x-4\right)^2}{2}-7\)

Ta có: \(-\frac{\left(2x-4\right)^2}{2}\le0\forall x\)

Đến đây b làm tương tự như trên nhé. 

Chúc b học tốt

a)  \(A=-x^2+6x-15\)

\(-A=x^2-6x+15\)

\(-A=\left(x^2-6x+9\right)+6\)

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

Mà  \(\left(x-3\right)^2\ge0\forall x\)

\(\Rightarrow-A\ge6\)

\(\Leftrightarrow A\le-6\)

Dấu "=" xảy ra khi :

\(x-3=0\Leftrightarrow x=3\)

Vậy  \(A_{Max}=-6\Leftrightarrow x=3\)

b) \(B=-2x^2+6x-15\)

\(-2B=4x^2-12x+30\)

\(-2B=\left(4x^2-12x+9\right)+21\)

\(-2B=\left(2x-3\right)^2+21\)

Mà  \(\left(2x-3\right)^2\ge0\forall x\)

\(\Rightarrow-2B\ge21\)

\(\Leftrightarrow B\le-\frac{21}{2}\)

Dấu "=" xảy ra khi :

\(2x-3=0\Leftrightarrow x=\frac{3}{2}\)

Vậy  \(B_{Max}=-\frac{21}{2}\Leftrightarrow x=\frac{3}{2}\)

a) (x+y+4).(x+y-4) = (x+y)² -16

phần b với phần c mình chưa học nên biết có vậy

a) (x + y + 4)(x + y - 4)
= [(x + y) + 4][(x + y) - 4]
= (x + y)² - 4²
= (x + y)2 - 16

b) Mình không biết có sai đề không nhưng mình không làm được câu này

c) (x + 2y + 3z)(2y + 3z - x)
= [(2y + 3z) + x][(2y + 3z) - x]
= (2y + 3z)² - x²

a) \(-y^2+\dfrac{1}{9}\)

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

\(=-\left(y+\dfrac{1}{3}\right)\left(y-\dfrac{1}{3}\right)\)

b) \(4^4-256\)

\(=4^4-4^4\)

\(=0\)

c) \(9\left(x-3\right)^2-4\left(x+1\right)^2\)

\(=\left(3x-9\right)^2-\left(2x+2\right)^2\)

\(=\left(3x-9+2x+2\right)\left(3x-9-2x-2\right)\)

\(=\left(5x-7\right)\left(x-11\right)\)

\(a,=\left(\dfrac{1}{3}-y\right)\left(\dfrac{1}{3}+y\right)\\ b,=\left(x^2-16\right)\left(x^2+16\right)\\ =\left(x-4\right)\left(x+4\right)\left(x^2+16\right)\\ c,=\left[3\left(x-3\right)-2\left(x+1\right)\right]\left[3\left(x-3\right)+2\left(x+1\right)\right]\\ =\left(3x-9-2x-2\right)\left(3x-9+2x+2\right)\\ =\left(x-11\right)\left(5x-7\right)\\ d,=\left(5x-\dfrac{1}{9}xy\right)\left(5x+\dfrac{1}{9}xy\right)=x^2\left(5-\dfrac{1}{9}y\right)\left(5+\dfrac{1}{9}y\right)\)

*Bạn ăn cơm chưa?

-Chưa.

*Hôm nay bạn đi đâu?

-Hà Nội.

*Bạn học lớp mấy?

-8.

*Bạn nghỉ học từ bao giờ?

-Sáng.

......................?

mik ko biết

mong bn thông cảm !$$%

\(\left(x+2\right)^2+\left(x-3\right)^2-2\left(x-1\right)\left(x+1\right)=9\)

<=> \(x^2+2x+4+x^2-6x+9-2\left(x^2-1\right)=9\)

<=> \(2x^2-4x+13-2x^2+2=9\)

<=> \(-4x+15-9=0\)

<=> \(-4x+6=0\)

<=> \(4x=6\)

<=> \(x=\frac{3}{2}\)

1. Nam doesn't like durians. Hoa doesn't like durians. ( Kết hợp câu dùng "neither")

=> Nam doesn't like durians and neither does Hoa.

2. Long likes orange juice. Linh likes orange juice. (Ket hợp câu dùng " too")

=> Long likes orange juice and Linh does, too.

3. Nam didn't watch TV last night. Hoa didn't watch TV last night. (Kết hợp câu dùng "either")

=> Nam didn't watch TV last night, Hoa didn't, either.

4. Hoa ate bread for breakfast. Her uncle ate bread for breakfast. (Kết hợp câu dùng " so")

=> Hoa ate bread for breakfast, so did her uncle.

5. He ought ( drive) .to drive.......more carefully (chia động từ)

6. You ought (do) .....to do....your homework before you play chess.(chia động từ)

7.Woula you like (play).....to play.... table tennis with me ? ( Chia động từ)

9.The children shouldn't ( stay)...stay... up late. (Chia đong từ )

9. Tuan is a careful cyclist. (Viet cau dung tu goi y)

=> Tuan cycles carefully.

10.His sisier plays badminton well. (Viet cau dung tu goi y)

=> His sister is a good badminton player.

11. My mother cooks excellently. (Viet cau su dung tu goi y)

=> My mother is an excellent cook.

12. My brother is good at speaking English. (Viet cau su dung tu goi y)

=> My brother speaks English well.

13. You should not watch T.V too late, ( Viet cau su dung tu goi y)

=> You ought not to watch TV too late.

Chọn B

B

Đề bài: Chọn đẳng thức đúng trong các đăng thức cho dưới đây