Bài 1.

\(a,\left(2^4\cdot3\cdot5^2\right):\left\{450:\left[450-\left(4\cdot5^3-2^3\cdot5^2\right)\right]\right\}\)

\(=\left(16\cdot3\cdot25\right):\left\{450:\left[450- \left(4\cdot125-8\cdot25\right)\right]\right\}\)

\(=\left(48\cdot25\right):\left\{450:\left[450-\left(500-200\right)\right]\right\}\)

\(=1200:\left[450:\left(450-300\right)\right]\)

\(=1200:\left(450:150\right)\)

\(=1200:3\)

\(=400\)

\(---\)

\(b,3^3\cdot5^2-20\left\{90-\left[164-2\cdot\left(7^8:7^6+7^0\right)\right]\right\}\)

\(=27\cdot25-20\left\{90-\left[164-2\cdot\left(7^2+1\right)\right]\right\}\)

\(=675-20\left\{90-\left[164-2\cdot\left(49+1\right)\right]\right\}\)

\(=675-20\left[90-\left(164-2\cdot50\right)\right]\)

\(=675-20\left[90-\left(164-100\right)\right]\)

\(=675-20\left(90-64\right)\)

\(=675-20\cdot26\)

\(=675-520\)

\(=155\)

\(---\)

\(c,\left[\left(18^7:18^6-17\right)\cdot2022-1986\right]\cdot5\cdot1^{2022}-13^2\cdot2020^0\)

\(=\left[\left(18-17\right)\cdot2022-1986\right]\cdot5\cdot1-169\cdot1\)

\(=\left(1\cdot2022-1986\right)\cdot5-169\)

\(=\left(2022-1986\right)\cdot5-169\)

\(=36\cdot5-169\)

\(=180-169\)

\(=11\)

Bài 2.

\(a) (2^x+1)^2+3\cdot(2^2+1)=2^2\cdot10\\\Rightarrow (2^x+1)^2+3\cdot(4+1)=4\cdot10\\\Rightarrow (2^x+1)^2+3\cdot5=40\\\Rightarrow (2^x+1)^2+15=40\\\Rightarrow (2^x+1)^2=40-15\\\Rightarrow (2^x+1)^2=25\\\Rightarrow (2^x+1)^2= (\pm 5)^2\\\Rightarrow \left[\begin{array}{} 2^x+1=5\\ 2^x+1=-5 \end{array} \right.\\ \Rightarrow \left[\begin{array}{} 2^x=4\\ 2^x=-6 (vô.lí) \end{array} \right. \\ \Rightarrow 2^x=2^2\\\Rightarrow x=2\)

Vậy \(x=2\).

\(---\)

\(b)3\cdot(x-7)+2\cdot(x+5)=41\\\Rightarrow 3\cdot x+3\cdot(-7)+2\cdot x+2\cdot5=41\\\Rightarrow 3x-21+2x+10=41\\\Rightarrow (3x+2x)+(-21+10)=41\\\Rightarrow 5x-11=41\\\Rightarrow 5x=41+11\\\Rightarrow 5x=52\\\Rightarrow x=\dfrac{52}{5}\)

Vậy \(x=\dfrac{52}{5}\).

\(Toru\)

a) 2(x-51) = 2^0.2^4 + 5.2^2

    2(x-51) = 2^2(2^2+5)

    2(x-51) = 36

       x-51  =  18

       x       = 69

Vậy: x = 69

b) 225 : (x-19) = 25

              x-19   = 9

              x        =  28

Vậy: x = 28

c) 4. (x-3)= 7^2-1^0

    4. (x-3)= 48

         x-3 = 12

        x     = 15

Vậy: x = 15

d) 3^3(x+4) - 3.5^2= 15.2^2

     27 (x+4) - 75     =   60

     27 (x+4)            =   135

           x+4             =    5

           x                 =     1

Vậy: x = 1

e) 2x-7^2 = 5.3^2

    2x - 49 = 45

    2x        = 94

      x        = 47

Vậy: x = 47

f) 2^3.5^2-(2x+6) = 4^3

   200 - 2x - 6       = 64

          194 - 2x     = 64

              2x          = 130

                x          = 65

Vậy: x = 65

g) 135 - 5(x+4) = 35

             5(x+4)  = 100

                x + 4 = 20

                x       =  16

Vậy: x = 16

h) 75 + 9(x-8) = 318

            9(x-8) = 243

              x-8   = 27

              x      = 35

Vậy: x = 35

2/3 x(5/7 + 1) +7/2 -1/3

=2/3x12/7 + 7/2 - 1/3

=8/7 +7/2-1/3

=(48+147-14)/3

= 181/42

2/3 x(5/7 + 1) +7/2 -1/3

=2/3x12/7 + 7/2 - 1/3

=8/7 +7/2-1/3

=(48+147-14)/3

= 181/42

Tick cho mình nha

pt ko có VP sao giải đây

VP và 3,5 à bạn chờ nhé

\(\Leftrightarrow2\left(8x+7\right)^2\left(4x+3\right)\left(x+1\right)=3,5\times2=7\)

\(\Leftrightarrow\left(8x+7\right)^2\left[2\left(4x+3\right)\right]\left[8\left(x+1\right)\right]=7\times8\)

Đặt t=8x+7.Pt trở thành:

\(t^2\left(t+1\right)\left(t-1\right)=56\)

\(\Leftrightarrow t^2\left(t^2-1\right)=56\)

\(\Leftrightarrow t^4-t^2-56=0\)

\(\Leftrightarrow t^4-8t^2+7t^2-56=0\)

\(\Leftrightarrow t^2\left(t^2-8\right)+7\left(t^2-8\right)=0\)

\(\Leftrightarrow\left(t^2-8\right)\left(t^2+7\right)=0\)

\(\Leftrightarrow t=8\)(vì t²+7>0)

Do đó 64x²+112x+41=0

Tới đây bạn denta hoặc vi-ét nó ra

\(\Leftrightarrow x=-\frac{\sqrt{2^3}+7}{8}\)hoặc\(x=\frac{\sqrt{2^3}-7}{8}\)

a) \(\left(x-1\right)^3=8=2^3\)

\(x-1=2\)

\(x=2+1=3\)

b) \(7^{2x-6}=49=7^2\)

\(2x-6=2\)

\(2x=6+2=8\)

\(x=8:2=4\)

c) \(\left(2x-14\right)^7=128=2^7\)

\(2x-14=2\)

\(2x=14+2=16\)

\(x=16:2=8\)

d) \(x^4\cdot x^5=5^3\cdot5^6=5^4\cdot5^5\)

\(x=5\)

e) \(3\cdot\left(x+2\right):7\cdot4=120\)

\(x+2=120:3\cdot7:4\)

\(x+2=70\)

\(x=70-2=68\)

Lời giải:

a. $(x-1)^3=8=2^3$
$\Rightarrow x-1=2$

$\Rightarrow x=3$

b. $7^{2x-6}=49=7^2$
$\Rightarrow 2x-6=2$

$\Rightarrow 2x=8$

$\Rightarrow x=4$

c. $(2x-14)^7=128=2^7$

$\Rightarrow 2x-14=2$

$\Rightarrow 2x=16$

$\Rightarrow x=18$

d.

$x^4.x^5=5^3.5^6$

$x^9=5^9$

$\Rightarrow x=5$

e. 

$3(x+2):7=120:4=30$

$3(x+2)=30.7=210$

$x+2=210:3=70$

$x=70-2=68$