cho ΔABC có góc BAC = 60 độ, AD là đường phân giác. Chứng minh rằng \(\frac{1}{AB}+\frac{1}{AC}=\frac{\sqrt{3}}{AD}\)

Cho M =\(\frac{x\sqrt{x}-1}{x-\sqrt{x}}-\frac{x\sqrt{x}+1}{x+\sqrt{x}}+\frac{x+1}{\sqrt{x}}\)

a) rút gọn M

b) Tìm x để M = \(\frac{9}{2}\)

c) So sánh M và 4

Cho A = \(\left(\frac{1}{\sqrt{x}-1}+\frac{\sqrt{x}}{x-1}\right).\frac{x-\sqrt{x}}{2\sqrt{x}+1}\)

a) rút gọn A

b) tính A khi x = 9

c) tìm x nguyên để A nguyên

d) tìm M để pt A = m có nghiệm

Cho biểu thức M = \(\left(\frac{2}{\sqrt{x}-3}+\frac{1}{\sqrt{x}+3}\right):\frac{\sqrt{x}+1}{\sqrt{x}-3}\)

a) Rút gọn Q

b) Tính M khi x = 4 - \(2\sqrt{3}\)

c) Tìm x để M = \(\frac{\sqrt{x}}{6}\)

d) Tìm GTLN của M

tìm giá trị nhỏ nhất của A = |x - 1| + 2|x - 2| + |x - 3| + 4

cho tam giác ABC có AD ⊥ BC, CK ⊥ AB. Chứng minh ΔACD ~ ΔBCK

cho tam giác ABC có AD ⊥ BC, CK ⊥ AB. Chứng minh ΔACD ~ ΔACK

Finish the second sentence in such a way that it means the same as the first

1. It took a long time for the patient to recover completely from his illness.

-> Only_______________

2. The cost of running that house would be beyond our means.

-> We couldn’t______________

3. The only thing I could do was sit and wait.

-> There was_________________

4. I find it impossible to see animals in pain.

-> I can’t stand_________________

5. I’m sure young children will love this new film. APPEAL

-> I’m sure_________________

Identify the underlined part that needs correction in each of the following sentences:

1. There's no chance at all that there will be many people at the meeting because it hasn’t been properly advertising.

2. Money can improve the condition of people who do not have enough cash to live comfortably. Therefore, money alone is not enough to bring happiness.