1a

\(A=\frac{3}{2ab}+\frac{1}{2ab}+\frac{1}{a^2+b^2}+\frac{a^4+b^4}{2}\ge\frac{6}{\left(a+b\right)^2}+\frac{4}{\left(a+b\right)^2}+\frac{\frac{\left(a^2+b^2\right)^2}{2}}{2}\)

\(\ge10+\frac{\left[\frac{\left(a+b\right)^2}{2}\right]^2}{4}=10+\frac{1}{16}=\frac{161}{16}\)

Dau '=' xay ra khi \(a=b=\frac{1}{2}\)

Vay \(A_{min}=\frac{161}{16}\)

1b.\(B=\frac{1}{2ab}+\frac{1}{2ab}+\frac{1}{a^2+b^2}+\frac{a^8+b^8}{4}\ge\frac{2}{\left(a+b\right)^2}+\frac{4}{\left(a+b\right)^2}+\frac{\frac{\left(a^4+b^4\right)^2}{2}}{4}\)

\(\ge6+\frac{\left[\frac{\left(a^2+b^2\right)^2}{2}\right]^2}{8}\ge6+\frac{\left[\frac{\left(a+b\right)^2}{2}\right]^2}{32}=6+\frac{1}{128}=\frac{769}{128}\)

Dau '=' xay ra khi \(a=b=\frac{1}{2}\)

Vay \(B_{min}=\frac{769}{128}\)khi \(a=b=\frac{1}{2}\)

a) \(\frac{\left(-3\right)^n}{81}=-27\)

     \(\left(-3\right)^n=81.\left(-27\right)\)

     \(\left(-3\right)^n=\left(-3\right)^4.\left(-3\right)^3\)

      \(\left(-3\right)^n=\left(-3\right)^7\)

         \(n=7\)

b) 

\(4< 2^n\le2.16\)

\(2^2< 2^n\le2^5\)

\(2< n\le5\)

\(n\in\left\{3;4;5\right\}\)

c) 

\(\frac{16^n}{4^n}=1024\)

\(\left(\frac{16}{4}\right)^n=4^5\)

\(4^n=4^5\)

\(n=5\)

a,17.4

=10.4 + 7.4

=40+28

=68

b.13.12

=13.10 + 13.2

=1300+26

=1326

53.11

=53.10 + 53

=5300+53

=5353

39.101

=39.100 + 39

=3900+39

=3939 (k cho mik vs)

\(a,\frac{(-10)^5}{3\cdot(-6)^4}=\frac{(-2\cdot5)^5}{3\cdot(-2\cdot3)^4}=\frac{(-2)^5\cdot5^5}{3\cdot(-2)^4\cdot3^4}=\frac{(-2)^5\cdot5^5}{(-2)^4\cdot3^5}=-2\cdot\frac{5^5}{3^5}=\frac{-6250}{243}\)

\(b,\frac{2^{15}\cdot9^4}{6^6\cdot8^3}=\frac{\left[2^3\right]^5\cdot\left[3^2\right]^4}{\left[3\cdot2\right]^6\cdot\left[2^3\right]^3}=\frac{2^{15}\cdot3^8}{3^6\cdot2^6\cdot2^9}=\frac{2^{15}\cdot3^8}{3^6\cdot2^{15}}=\frac{3^8}{3^6}=3^2=9\)

\(c,\left[1+\frac{2}{3}-\frac{1}{4}\right]\cdot\left[\frac{4}{5}-\frac{3}{4}\right]^2\)

\(=\left[\frac{12}{12}+\frac{8}{12}-\frac{3}{12}\right]\cdot\left[\frac{16}{20}-\frac{15}{20}\right]^2\)

\(=\frac{17}{12}\cdot\left[\frac{1}{20}\right]^2=\frac{17}{12}\cdot\frac{1^2}{20^2}=\frac{17}{12}\cdot\frac{1}{400}=\frac{17}{4800}\)

\(d,2^3+3\cdot\left[\frac{1}{2}\right]^0+\left[(-2)^2:\frac{1}{2}\right]\)

\(=8+3\cdot\frac{1^0}{2^0}+\left[4:\frac{1}{2}\right]\)

\(=8+3\cdot1+8=8+3+8=19\)

B1:

a. (x - 45) . 27 = 0

     x - 45 = 0

     x = 45

b. 23 . (42 - x) = 23

    42 - x = 1

     x = 41

Bài 1 : 

( x - 45 ) . 27 = 0 

( x - 45 )        = 0 : 27 

 x - 45        =  0

x - 45         = 0 

x                = 0 + 45 

x               = 45 

23 . ( 42 - x ) = 23

( 42 - x )       = 23 : 23

 42 - x        = 1

 x        =  42 - 1 

x        = 41 

~ Còn tiếp 

Trả lời :

\(\left[\left(\frac{-3}{4}\right)^3\right]^2\)

\(=\left[-\frac{27}{64}\right]^2\)

\(=\frac{729}{4096}\)

Study well 

\(=\left[-\frac{27}{64}\right]^2\)

\(=\frac{729}{4096}\)

Học tốt

số bé là: 516:(7-1)  x 1 -  36=50

số lớn  là:50+516=566

Nếu viết thêm vào mỗi số 36 đv thì hiệu 2 số ko đổi, vẫn = 516.

Xem SB sau khi thêm là 1 phần thì SL sau khi thêm là 7 phần như thế.

SB à:

        516 : ( 7 - 1 ) - 36 = 50

SL là:

      516 - 50 = 466

            Đs : SL : 466

                   SB: 50