Cho các số thực không âm a. b. c thỏa mãn a + b + c = 3

TÌm GTLN của P = \(a\sqrt{b}+b\sqrt{c}+c\sqrt{a}-\sqrt{abc}\)

Cách 1:

Vì D là trung điểm của AC => BD là đường trung tuyến ΔABC

Xét ΔABC cân tại B có BD là đường trung tuyến => BD là tia phân giác của góc B

Cách 2:

Vì D là trung điểm AC => AD = CD

Vì ΔABC cân tại B => \(\left\{{}\begin{matrix}AB=AC\\\widehat{BAC}=\widehat{BCA}\Rightarrow\widehat{BAD}=\widehat{BCD}\end{matrix}\right.\)

Xét ΔBAD và ΔBCD có:

AB = AC (gt)

\(\widehat{BAD}=\widehat{BCD}\) (gt) 

AD = CD (gt) 

=> ΔBAD = ΔBCD (c.g.c)

=> \(\widehat{ABD}=\widehat{CBD}\) (cặp góc tương ứng)

=> BD là tia phân giác của góc B

a, \(\dfrac{6}{x-3}=\dfrac{9}{2x-7}\)

=> 6(2x-7) = 9(x-3)

=> 12x - 42 = 9x - 27

=> 12x - 9x = -27 + 42

=> 3x = 15 

=> x = 5

Vậy x = 5

b, \(\dfrac{-7}{x+1}=\dfrac{6}{x+27}\)

=> -7(x + 27) = 6(x + 1)

=> -7x - 189 = 6x + 6

=> -7x - 6x = 6 + 189

=> -13x = 195

=> x = -15

Vậy x = -15

Dear Jun,

How are things? I hope you are doing well. I'm interested in showing how amazing it was when I spent my time on Tet.

As you know, Tet is considered the biggest festival of the year and the Vietnamese celebrate it annually to welcome the new year. We often get 5 or even 10 days off to celebrate Tet. Before this holiday, we decorate our house with colored - string lights and colorful flowers which were bought some days before. I really enjoyed it when I could go shopping to get new clothes with my mother and prepare for Tet. We also make "Chung" cake and cook a great variety of dishes. Then, Tet came and I was happy to spend my quality time with my loved one. I had a chance to share meals with my friends and family or enjoyed time watching fireworks with them on new year's eve. That was so amazing! On the first day of the new year, I dressed up my new clothes, visited my relatives to say: "Happy new year" and received lucky money in the red envelope from adults. After that, we went to the pagoda and wish for health, wealth, and luck prosperity for our family. Moreover, I could also listen to the stories about how our ancestors celebrated Tet in the past and ride a bike around the street with my friends. We had a lot of inspirational and memorable moments during Tet.

What about you? Don't hesitate to contact me.

Best wishes,

NA

150cm