a) \(5^{x+3}+5^x=126\)

\(\Rightarrow5^x\cdot\left(5^3+1\right)=126\)

\(\Rightarrow5^x\cdot\left(125+1\right)=126\)

\(\Rightarrow5^x=\dfrac{126}{126}\)

\(\Rightarrow5^x=1\)

\(\Rightarrow5^x=5^0\)

\(\Rightarrow x=0\)

b) \(\dfrac{9-3x}{2}=\dfrac{5-2x}{3}\)

\(\Rightarrow\dfrac{3\cdot\left(9-3x\right)}{6}=\dfrac{2\cdot\left(5-2x\right)}{6}\)

\(\Rightarrow3\cdot\left(9-3x\right)=2\cdot\left(5-2x\right)\)

\(\Rightarrow27-9x=10-4x\)

\(\Rightarrow-4x+9x=27-10\)

\(\Rightarrow5x=17\)

\(\Rightarrow x=\dfrac{17}{5}\)

c) \(7-4\left(x+1\right)=5\)

\(\Rightarrow4\left(x+1\right)=7-5\)

\(\Rightarrow4\left(x+1\right)=2\)

\(\Rightarrow x+1=\dfrac{1}{2}\)

\(\Rightarrow x=\dfrac{1}{2}-1\)

\(\Rightarrow x=-\dfrac{1}{2}\)

A/ 15+(3-x)=-10

      15+3-x=-10

       18-x=-10

         -x=-10-18=-8

Suy ra x= 8 

a, 15 + (3-x) = -10

            3-x  = -10 - 15

            3-x  = -25

               x  = 3 - (-25)

               x  = -28

b, 11 - ( 53 + x ) = 97

          53 + x     = 11 - 97

          53 + x     = -86

                 x      = -86 - 53

                 x      =   -139

c, 5x - (-25) = 35

    5x          =35 + ( -25)

    5x          =   10

     x           = 10 : 5

     x           = 2

a,

15 + ( 3 - x ) = - 10

          3 - x   = - 10 - 15

          3 - x = - 25

               x = 3 - ( - 25 )

               x = 28

b, 11 - ( 53 + x ) = 97

            53 + x   = 11 - 97

            53 + x   = - 86

                    x   = - 86 - 53

                    x   = - 139

c, 5x - ( - 25 ) = 35

    5x             = 35 + ( - 25 )

    5x             = 10

      x             = 10 : 5

      x             = 2

Bài 1: Ta có: \(53^2-53\cdot6+3^2\)

\(=53^2-2\cdot53\cdot3+3^2\)

\(=\left(53-3\right)^2\)

\(=50^2=2500\)

Bài 2: Ta có: \(-x^2+x-33\)

\(=-\left(x^2-x+33\right)\)

\(=-\left(x^2-2\cdot x\cdot\frac{1}{2}+\frac{1}{4}+\frac{131}{4}\right)\)

\(=-\left(x-\frac{1}{2}\right)^2-\frac{131}{4}\)

Ta có: \(\left(x-\frac{1}{2}\right)^2\ge0\forall x\)

\(\Rightarrow-\left(x-\frac{1}{2}\right)^2\le0\forall x\)

\(\Rightarrow-\left(x-\frac{1}{2}\right)^2-\frac{131}{4}\le\frac{131}{4}< 0\forall x\)

hay \(-x^2+x-33< 0\forall x\)(đpcm)

Bài 3: Ta có: \(x^2+4x+33\)

\(=x^2+4x+4+29\)

\(=\left(x+2\right)^2+29\)

Ta có: \(\left(x+2\right)^2\ge0\forall x\)

\(\Rightarrow\left(x+2\right)^2+29\ge29>0\forall x\)

hay \(x^2+4x+33>0\forall x\)

Bài 4: Ta có: \(B=x^2+8x\)

\(=x^2+8x+16-16\)

\(=\left(x+4\right)^2-16\)

Ta có: \(\left(x+4\right)^2\ge0\forall x\)

\(\Rightarrow\left(x+4\right)^2-16\ge-16\forall x\)

Dấu '=' xảy ra khi x+4=0

hay x=-4

Vậy: Giá trị nhỏ nhất của biểu thức \(B=x^2+8x\) là -16 khi x=-4

Bài 5: Tìm x

Ta có: \(\left(5x+1\right)^2-\left(5x+3\right)\left(5x-3\right)=30\)

\(\Leftrightarrow25x^2+10x+1-\left(25x^2-9\right)-30=0\)

\(\Leftrightarrow25x^2+10x+1-25x^2+9-30=0\)

\(\Leftrightarrow10x-20=0\)

\(\Leftrightarrow10x=20\)

hay x=2

Vậy: x=2

x+1+5x-2=53

6x-1=53

6x=54

x=9

Đáp án: B

25+5x= 5 6 : 5 3

25+5x=53

25+5x=125

5x=125-25

5x=100

x=100:5

x=20

Bài 1: 

a: =42x53+47x42

=42x100

=4200

b: =1152-374-1152-65+374=-65

c: =(-1)+(-1)+...+(-1)+211

=211-105

=106

1/

a)5x – 20y=5(x-4y)

b) 5x.(x –  1) –  3x(x – 1)=2x(x-1)

c) x.(x+y) – 5x – 5y=c) x.(x+y) – 5(x+y)=(x-5)(x+y)

2/

a)x² + xy + x = x(x+y+1)=77.(77+22+1)=77.100=7700

b)  x . ( x – y ) + y . ( y – x )=(x-y)(x-y)=(x-y)²=(53-3)²=2500

3/

a) X + 5x² = 0

⇒x(x+5)=0

⇒hoặc x=0

x+5=0⇒x=-5

b)x + 1 = ( x + 1 )² 

⇒(x + 1)-( x + 1 )² =0

⇒x(x+1)=0

⇒ hoặc x=0

hoặc x+1=0⇒x=-1

4/

a) 97 . 13 + 130 . 0,3 = 97.13+13.10.0,3=97.13+13.3=100.13=1300

b)86 . 153 – 530 . 8,6=86.153–53.10.8,6=86.153-53.86=86.100=8600

C) 85 .12,7 + 5,3 . 12,7= 12,7(85+5,3)=12,7.90,3=1146,81

D)52.143 – 52 . 39 – 8.26=52(143-39)-8,26=52.104-8,26=5399,74

Bài 1:  

a) 5x-20y=5(x-4y)

b) \(5x\left(x-1\right)-3x\left(x-1\right)=2x\left(x-1\right)\)

c) \(x\left(x+y\right)-5x-5y=\left(x+y\right)\left(x-5\right)\)

Bài 2: 

a) \(x^2+xy+x\)

\(=x\left(x+y+1\right)\)

\(=77\cdot\left(77+22+1\right)\)

=7700

b) \(x\left(x-y\right)+y\left(y-x\right)\)

\(=x\left(x-y\right)-y\left(x-y\right)\)

\(=\left(x-y\right)^2\)

\(=50^2=2500\)

Đáp án cần chọn là: B

720 : [41 - (2x - 5)] = 8 . 5

=> 720 : [41 - (2x - 5)] = 40

=> 41 - (2x - 5) = 720 : 40

=> 41 - (2x - 5) = 18

=> 2x - 5 = 41 - 18

=> 2x - 5 = 23

=> 2x = 23 + 5

=> 2x = 28

=> x = 28 : 2

=> x = 14

Vậy x = 14

1 + 2 + 3 + 4 + ... + (x - 1) + x = 78

            có x số hạng

=> (x + 1) . x : 2 = 78

=> (x + 1) . x = 78 . 2

=> (x + 1) . x = 156

=> (x + 1) . x = 13 . 12

=> x = 12

Vậy x = 12