Cho: a, b, c > 0; ab + bc + ca = 1.

Tìm max của: A = \(\frac{x}{\sqrt{x^2+1}+x}\)+ \(\frac{y}{\sqrt{y^2+1}+y}\)+ \(\frac{z}{\sqrt{z^2+1}+z}\)

Cho: a, b, c > 0; a + b + c = abc.

Tìm max của: A = \(\dfrac{1}{\sqrt{1+c^2}}\) + \(\dfrac{1}{\sqrt{a^2+1}}\) + \(\dfrac{1}{\sqrt{b^2+1}}\)

Cho tam giác ABC có I là giao điểm 3 đường phân giác. CMR: AI + AC = BC

cho tam giác ABC. kẻ phân giác trong BD, CK. từ A kẻ đường thẳng vuông góc với CK tại M, từ A, C kẻ các đường thẳng vuông góc với BD tại N và L tương ứng, MN cắt AC tại E, BF cắt CL tại E

a, chứng minh MN//BC

b, chứng minh LF//AB và LF đi qua trung điểm BC

c, chứng minh DE//BC

Tính:

P=\(\dfrac{1}{\sqrt{2}.1+\sqrt{1}.2}\)+\(\dfrac{1}{\sqrt{3}.2+\sqrt{2}.3}\)+\(\dfrac{1}{\sqrt{4}.3+\sqrt{3}.4}\)+...+\(\dfrac{1}{\sqrt{100}.99+\sqrt{99}.100}\)

Cho a, b, c ϵ Z

a²+b²+c²=2(ab+bc+ca)

CMR: ab, bc, ca là số chính phương

CMR: không tồn tại x, y, z ϵ Q phân biệt thỏa mãn:

\(\dfrac{1}{\left(x-y\right)^2}\)+\(\dfrac{1}{\left(y-z\right)^2}\)+\(\dfrac{1}{\left(z-x\right)^2}\)=2018

Với y = 5 thì giá trị của biểu thức 168 – y × 5 là:

A. 815

B. 143

C. 193

D. 161

Rewrite the following sentences using the words in brackets

1. She couldn't do everything she was supposed to do (failed)

2. My sister is unlikely to win the first prize in the singing contest (likehood)

3. I don't think there will be any applicants for this post (likehood)

4. It's possible that you will get what you want there (chance)

5. He didn;t say aanything about his new job when I last spoke to him (reference)

Mark the letter A, B, C, or D on your answer sheet to indicate the sentence that is closest in meaning to each of the following questions.

“ You should take more care of your health or you may regret it,” the doctor said to her.

A. She might regret taking more care of her health, which was the doctor’s advice to her.

B. The doctor advised her to take more care of her health or she might regret it.

C. The doctor recommened her taking more care of her health so that she wouldn’t regret it.

D. It will be a good idea if she takes more care of her health, otherwise she might regret it.