Chào em, em tham khảo nhé!

1.l can't finish this task if you don't give me a hand.

=> Unless you give me a hand, I can't finish this task.

2.You will run out of money if you don't stop wasting it.

=> Unless you stop wasting money, you will run out of it.

3.Don't call me unless it is an emergency.

=> If it is not an emergency, don't call me.

4.James will not pass the test unless he studies harder.

=> If Jame doesn't study harder, he will not pass the test.

5.If Jane finishes her work before 6 pm, she will dine out with her friends.

=> Unless Jane finishes her work before 6 pm, she will not dine out with her friends.

Chúc em học tốt và có những trải nghiệm tuyệt vời tại olm.vn!

1. I would be surprised if Ann came to see us now.

2. If we had enough money,we would go on holiday

3. Unless you do these exercises more carefully, you will fail the exam.

4. If I knew the answer, I could tell you.

5. If she knew French, she could apply for the job

6. Unless she cam here now, we'd come back home

7. Unless you are careful, you will be able to get the job

8. If it rains soon, the tree won't die

* Rewrite the sentences.

1. It is late now; I don't think Ann will come to see us.

-> I would be surprised if __________Ann came to see us________.

2. We don't go on holiday because we don't have enough money.

-> If _________we had enough money, we would go on holiday_________.

3. Do these exercises more carefully or you will fail the exams.

->Unless_________you do these exercises more carefully, you will fail the exams_________.

4. I do not know the answer so I cannot tell you.

-> If _________I knew the answer, I could tell you_________.

5. She can't apply for the job because she doesn't know Frencj.

-> If she knew__________Frencj, she could apply for the job________.

6. If she didn't come here now, we'd come back home.

-> Unless__________she came here now, we'd come back home________.

7. Be careful or you will not be able to get the job.

-> Unless__________you are careful, you won't be able to get the job________.

8. The trees will die unless it rains soon.

-> If_________it doesn't rain soon, the trees will die_________.

Yêu cầu:tìm x

Với x \(\inℕ\)ta có : 1 + x(x + 2) = x² + 2x + 1 = (x + 1)²

Ta có \(\left(1+\frac{1}{1.3}\right)\left(1+\frac{1}{2.4}\right)\left(1+\frac{1}{3.5}\right)...\left(1+\frac{1}{x\left(x+2\right)}\right)=\frac{31}{16}\)

=> \(\left(\frac{1+1.3}{1.3}\right)\left(\frac{2.4+1}{2.4}\right)\left(\frac{3.5+1}{3.5}\right)....\left(\frac{x\left(x+2\right)+1}{x\left(x+2\right)}\right)=\frac{31}{16}\)

=> \(\frac{2^2}{1.3}.\frac{3^2}{2.4}.\frac{4^2}{3.5}....\frac{\left(x+1\right)^2}{x\left(x+2\right)}=\frac{31}{16}\)

=> \(\frac{2^2.3^2.4^2...\left(x+1\right)^2}{1.3.2.4.3.5...x\left(x+2\right)}=\frac{31}{16}\)

=> \(\frac{\left(2.3.4...\left(x+1\right)\right).\left(2.3.4....\left(x+1\right)\right)}{\left(1.2.3...x\right)\left(3.4.5...\left(x+2\right)\right)}=\frac{31}{16}\)

=> \(\frac{\left(x+1\right).2}{x+2}=\frac{31}{16}\)

=> 31(x + 2) = (x + 1).2.16

=> 31x + 62 = (x + 1).32

=> 31x + 62 = 32x + 32

=> 32x - 31x = 62 - 32

=> x = 30

Vậy x = 30

Giải phương trình nhé!

Ta có x³ - y³ + z³ + 3xyz

= (x - y)(x² + xy + y²) + z³ + 3xyz

= (x - y)³ + 3xy(x - y) + z³ + 3xyz

= [(x - y)³ + z³] + (3xy(x - y) + 3xyz)

= (x - y + z)[(x - y)² - (x - y).z + z²] + 3xy(x - y + z)

= (x - y + z)[x² - 2xy + y² - xz + yz + z²] + 3xy(x - y + z)

= (x - y + z)(x² + y² + z² + xy + yz - zx)

Lại có (x + y)² + (y + z)² + (z - x)²

= x² + y² + 2xy + y² + z² + 2yz + z² - 2xz + x²

= 2x² + 2y² + 2z² + 2xy + 2yz - 2zx

= 2(x² + y² + z² + xy + yz - zx)

Khi đó \(\frac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}=\frac{\left(x-y+z\right)\left(x^2+y^2+z^2+xy+yz-zx\right)}{2\left(x^2+y^2+z^2+xy+yz-zx\right)}\)

\(=\frac{x-y+z}{2}\)

Đặt \(A=\frac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)

Xét tử, ta có: 

\(x^3-y^3+z^3+3xyz=\left(x-y\right)^3+3xy\left(x-y\right)+z^3+3xyz\)

\(=\left(x-y\right)^3+z^3+3xy\left(x-y\right)+3xyz\)

\(=\left(x-y+z\right)^3-3\left(x-y\right).z\left(x-y+z\right)+3xy\left(x-y+z\right)\)

\(=\left(x-y+z\right)\left[\left(x-y+z\right)^2-3\left(x-y\right)z+3xy\right]\)

\(=\left(x-y+z\right)\left(x^2+y^2+z^2-2xy-2yz+2xz-3xz+3yz+3xy\right)\)

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

Xét mẫu, ta có: 

\(\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2\)

\(=x^2+2xy+z^2+y^2+2yz+z^2+z^2-2xz+x^2\)

\(=2x^2+2y^2+2z^2+2xy+2yz-2xz\)

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

\(\Rightarrow A=\frac{x-y+z}{2}\)

sai đề rồi nhé , đề phải là :

\(\frac{x^3-y^3+z^3+3xyz}{\left(x+y\right)^2+\left(y+z\right)^2+\left(z-x\right)^2}\)

\(=\frac{\left(x-y\right)^3+3xy.\left(x-y\right)+z^3+3xyz}{x^2+2xy+y^2+y^2+2yz+z^2+z^2-2xz+x^2}\)

\(=\frac{\left(x-y+z\right).\left[\left(x-y\right)^2-\left(x-y\right).z+z^2\right]+3xy.\left(x-y+z\right)}{2x^2+2y^2+2z^2+2xy+2yz-2xz}\)

\(=\frac{\left(x-y+z\right).\left(x^2-2xy+y^2-xz+yz+z^2+3xy\right)}{2.\left(x^2+y^2+z^2+xy+yz-xz\right)}\)

\(=\frac{\left(x-y+z\right).\left(x^2+y^2+z^2+xy+yz-xz\right)}{2.\left(x^2+y^2+z^2+xy+yz-xz\right)}\)

\(=\frac{x-y+z}{2}\)