\(\dfrac{9}{10}\times2+3\times\dfrac{9}{10}+\dfrac{9}{10}:\dfrac{1}{5}\)

\(=\dfrac{9}{10}\times2+\dfrac{9}{10}\times3+\dfrac{9}{10}\times5\)

\(=\dfrac{9}{10}\times\left(2+3+5\right)\)

\(=\dfrac{9}{10}\times10\)

\(=\dfrac{90}{10}\)

\(=9\)

\(3^x.\left(3^2+1\right)=10\)

\(3^x.10=10\)

\(3^x=1\Rightarrow x=0\)

\(\Leftrightarrow2x\left(x+5\right)-3\left(x-2\right)=7x+1\)

\(\Leftrightarrow2x^2+10x-3x+6-7x-1=0\)

\(\Leftrightarrow2x^2+5=0\)(vô lý)

ĐKXĐ:\(\left\{{}\begin{matrix}x\ne2\\x\ne-5\end{matrix}\right.\)

\(\dfrac{2x}{x-2}-\dfrac{3}{x+5}=\dfrac{7x+1}{x^2+3x-10}\\ \Leftrightarrow\dfrac{2x\left(x+5\right)}{\left(x+5\right)\left(x-2\right)}-\dfrac{3\left(x-2\right)}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x^2-2x+5x-10}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}=\dfrac{7x+1}{x\left(x-2\right)+5\left(x-2\right)}\\ \Leftrightarrow\dfrac{2x^2+10x}{\left(x+5\right)\left(x-2\right)}-\dfrac{3x-6}{\left(x+5\right)\left(x-2\right)}-\dfrac{7x+1}{\left(x+5\right)\left(x-2\right)}=0\)

\(\Leftrightarrow\dfrac{2x^2+10x-3x+6-7x-1}{\left(x+5\right)\left(x-2\right)}=0\\ \Leftrightarrow\dfrac{2x^2+5}{\left(x+5\right)\left(x-2\right)}=0\\ \Rightarrow2x^2+5=0\left(vô.lí\right)\)

Vậy pt vô nghiệm

a) x - 1/2 = 3/5

x = 3/5 + 1/2

x = 11/10

b) x - 1/2 = -2/3

x = -2/3 + 1/2

x = -1/6

c) 2/5 - x = 0,25

x = 2/5 - 0,25

x = 2/5 - 1/4

x = 3/20

3/10 x 5/7 - 3/5 x 75/14

=3/14 - 45/14

= -3

1. Tìm x

a) 1+2+3+...+x = 210

=> \(\frac{x\left(x+1\right)}{2}=210\)

=> x = 20

b) \(32.3^x=9.3^{10}+5.27^3\)

=>\(32.3^x=9.3^{10}+5.3^9\)(\(27^3=\left(3^3\right)^3=3^9\))

=>\(32.3^x=9.3.3^9+5.3^9\)

=>\(32.3^x=3^9\left(9.3+5\right)\)

=>\(32.3^x=3^9.32\)

=>x = 9

2.

Ta có 2A = 3A - A

=> 2A = \(3\left(1+3+3^2+3^3+....+3^{10}\right)\)\(-\)\(1-3-3^2-3^3-....-3^{10}\)

=> 2A = \(3+3^2+3^3+.....+3^{11}-\)\(1-3-3^2-3^3-...-3^{10}\)

=> 2A = \(3^{11}-1\)

=> 2A+1 = \(3^{11}-1+1\)=\(3^{11}\)

=> n = 11

Ta có : a)1 + 2 + 3 + ... + x = 210

=> \(\frac{x\left(x+1\right)}{2}=210\)

=> x(x + 1) = 420

=> x(x + 1) = 20.21

=> x = 20

1/ 

a) \(1+2+3+...+x=210\)

\(\Rightarrow\frac{x.\left(x+1\right)}{2}=210\)

\(\Rightarrow x.\left(x+1\right)=210.2=420\)

\(\Rightarrow x^2+x=420\)

\(\Rightarrow x^2+x=400+20=20^2+20\Leftrightarrow x=20\)

b) \(32.3^x=9.3^{10}+5.27^3\)

\(\Rightarrow32.3^x=629856\)

\(\Rightarrow3^x=629856:32=19683=3^9\)

\(\Rightarrow x=9\)

2/

\(A=1+3+3^2+3^3+...+3^{10}\)

\(\Rightarrow A=3^0+3^1+3^2+3^3+...+3^{10}\)

\(\Rightarrow A=\frac{3^{10+1}-1}{3-1}=88573\)

Tìm n:

\(2.A+1=3^n\Rightarrow2.88573+1=3^n\)

\(\Rightarrow177147=3^n\Leftrightarrow3^{11}=3^n\Leftrightarrow n=11\)

   1a. ( 2¹⁰ + 1 )¹⁰ chia hết cho 125 = ( 1024 + 1 ) ¹⁰  chia hết cho 125 = 1025¹⁰ chia hết cho 125 

Ta có : 1025 : 125 = 8.2 nên 1025¹⁰ không thể chia hết cho 125 vì a chia hết cho b thì a nhân x chia hết cho b

   1b. 10²⁰¹⁸ + 5³ chia hết cho 9 = ( 1 + 0 + 0 + 0 + ... ) + 125 = 1 + 8 = 9 nên 10²⁰¹⁸ + 5³ chia hết cho 9

   2. x = 1 vì A =( 1 + 3 ) + ( 1 + 7 ) + ( 1 + 11 ) = 4 + 8 + 12 = 24

   Đây là đáp án mình làm thao khả năng của mk. Với lại câu 2 ko ghi rõ nên mk ko thể là chắc chắn đc  

câu a/

-10-(x-5)+(3-x)=-8

-10-x+5+3-x=-8

-2x=-8-3-5+10

-2x=-6

x=3

câu b/

10+3(x-1)=10+6x

10+3x-3=10+6x

3x-6x=10+3-10

-3x=3

x=-1

-10 -(x-5) + (3-x)=-8\(\Rightarrow\)(3-x)-(x-5)=2\(\Rightarrow\)

3-x-x+5=2\(\Rightarrow\)-2x+8=2\(\Rightarrow\)-2x=-6\(\Rightarrow\)x=-6:-2\(\Rightarrow\)x=3