áp dụng cô si ta có:

+)\(\frac{a^5}{b^3}+\frac{a^3}{b}\ge\frac{2a^4}{b^2};\frac{b^5}{c^3}+\frac{b^3}{c}\ge\frac{2b^4}{c^2};\frac{c^5}{a^3}+\frac{c^3}{a}\ge\frac{2c^4}{a^2}\)

\(\Leftrightarrow\frac{a^5}{b^3}+\frac{b^5}{c^3}+\frac{c^5}{a^3}\ge2\left(\frac{a^4}{b^2}+\frac{b^4}{c^2}+\frac{c^4}{a^2}\right)-\left(\frac{a^3}{b}+\frac{b^3}{c}+\frac{c^3}{a}\right)\)

+)\(\frac{a^4}{b^2}+a^2\ge\frac{2a^3}{b};\frac{b^4}{c^2}+b^2\ge\frac{2b^3}{c};\frac{c^4}{a^2}+c^2\ge\frac{2C^3}{a}\)

\(\Leftrightarrow\frac{a^4}{b^2}+\frac{b^4}{c^2}+\frac{c^4}{a^2}\ge2\left(\frac{a^3}{b}+\frac{b^3}{c}+\frac{c^3}{a}\right)-\left(a^2+b^2+c^2\right)\)

+)\(\frac{a^3}{b}+ab\ge2a^2;\frac{b^3}{c}+bc\ge2b^2;\frac{c^3}{a}+ca\ge2c^2\)

\(\Leftrightarrow\frac{a^3}{b}+\frac{b^3}{c}+\frac{c^3}{a}\ge\left(a^2+b^2+c^2\right)+\left(a^2+b^2+c^2-ab-bc-ca\right)\ge\left(a^2+b^2+c^2\right)\)

\(\Leftrightarrow\frac{a^4}{b^2}+\frac{b^4}{c^2}+\frac{c^4}{a^2}\ge\left(\frac{a^3}{b}+\frac{b^3}{c}+\frac{c^3}{a}\right)+\left(\frac{a^3}{b}+\frac{b^3}{c}+\frac{c^3}{a}-a^2-b^2-c^2\right)\ge\frac{a^3}{b}+\frac{b^3}{c}+\frac{c^3}{a}\)

\(\Leftrightarrow\frac{a^5}{b^3}+\frac{b^5}{c^3}+\frac{c^5}{a^3}\ge\left(\frac{a^4}{b^2}+\frac{b^4}{c^2}+\frac{c^4}{a^2}\right)+\left(\frac{a^4}{b^2}+\frac{b^4}{c^2}+\frac{c^4}{a^2}-\frac{a^3}{b}-\frac{b^3}{c}-\frac{c^3}{a}\right)\ge\left(\frac{a^4}{b^2}+\frac{b^4}{c^2}+\frac{c^4}{a^2}\right)\)

giải nhanh giúp mình với ạ 1) TÍNH: a) -9/34: 17/4 ; b) 1/1/2(hỗn số) . 1/24 ; c) -5/2: 3/4 ; d) 4/1/5 : (-2/4/5) 2) TÍNH: a) 3/5 + (-4/3) + ( -3/4) ; b) -7/2 + ( -2/3) + (-3/5); c) 3/4 - [(-5/3) - (1/12 + 2/9)] 3) TÌM x : a) 11/12 - (2/5+x) = 2/3 4) a) ( -3/4 + 2/5 ) : 3/7 + ( 3/5 + -1/4 ) : 3/7 b) 7/8 : ( 2/9 - 1/18 ) + 7/8 : ( 1/36 - 5/12 )

Bài 1: Tính

a, A = 7 + 7^3 + 7^5 + ...... + 7^151

b, B = 11^4 + 11^5 + 11^6 + ....... + 11^50

c, C = ( 2/3 )^4 + ( 2/3 )^5 + ( 2/3 )^6 + ..... + ( 2/3 )^100    ( 2/3 nghĩa là 2 phần 3 )

d, D = 5^100 - 5^99 - 5^98 - 5^97 -.....- 5^2 - 5 - 1

Bài 2: Cho A = 1 + 4 + 4^2 + ..... + 4^99

                  B = 4^100

a, Tìm B - A

b, Chứng minh rằng A < B/3   ( B/3 nghĩa là B phần 3 )

Bài 3 : Tính

a, A = 7^2 + 14^2 + 21^2 + 28^2 + ...... + 371^2

b, B = 11^2 + 22^2 + 33^2 + ...... + 1661^2

Bài 4 : Tính 

A = 99 x 1 + 98 x 2 + 97 x 3 + ....... + 3 x 97 + 2 x 98 +1 x 99

bài 1 : tính :  a. 3  2/5 - 1/2     b. 4/5 + 1/5 x 3/4     c. 4  4/9 : 2 2/3 + 3 1/6   d.  3 1/5 + 2 3/5 - 2 4/5 

bài 2 :đặt tính rồi tính : 3 2/5 + 2 1/5     b. 7 1/6 : 5 2/3 

bài 3 ; điền dấu > , <, = 

a. 800 kg 5 g ...8, 005 kg                             c. 5m 5mm .. 5 ,0005 m

b . 9 ha 4 dam2 . 9  5/100 ha                        d. 250kg ... 1/5 tấn 

giúp mình vs . mình cảm ơn các bạn