\(\Leftrightarrow10\left(2x-1\right)+6x=9x\\ \Leftrightarrow20x-10-3x=0\\ \Leftrightarrow17x=10\\ \Leftrightarrow x=\dfrac{10}{17}\)

a) (81-2)/1 + 1=80
b)(102-2)/1+1=101

a, x²-2x+2>0

⇔(x²-2x+1)+1>0(luôn đúng)

a. x² - 2x + 2 > 0

⇔ (x² - 2x + 1) + 1 > 0

Câu 9: D

Câu 10: A

a) \(7^6+7^5-7^4=\left(7^4.7^2\right)+\left(7^3.7^2\right)-\left(7^2.7^2\right)=7^2\left(7^4+7^3+7^2\right)=7^2.1793\)

Mà 1793 chia hết cho 11 => 7².1793 chia hết cho 11

b) \(10^9+10^8+10^7=\left(10^3.10^6\right)+\left(10^2.10^6\right)+\left(10.10^6\right)=10^6.\left(10^3+10^2+10\right)=10^6.1110\)

Mà 1110 chia hết cho 222 => 10⁶.1110 chia hết cho 222

x - ( 81 + 5x ) = 19

=> x - 81 - 5x = 19

=> ( x - 5x ) - 81 = 19

=> -4x = 19 + 81

=> -4x = 100

=> x = 100 : ( -4 )

=> x = -25

2x - ( 8 + 3x ) = 92

=> 2x - 8 - 3x = 92

=> ( 2x - 3x ) = 8 + 92

=> -x = 100

=> x = -100

a)ĐKXĐ: \(x\notin\left\{0;-1\right\}\)

Ta có: \(\dfrac{x-1}{x}+\dfrac{1}{x+1}=\dfrac{2x-1}{x^2+x}\)

\(\Leftrightarrow\dfrac{\left(x-1\right)\left(x+1\right)}{x\left(x+1\right)}+\dfrac{x}{x\left(x+1\right)}=\dfrac{2x-1}{x\left(x+1\right)}\)

Suy ra: \(x^2-1+x-2x+1=0\)

\(\Leftrightarrow x^2-x=0\)

\(\Leftrightarrow x\left(x-1\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x-1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\left(loại\right)\\x=1\left(nhận\right)\end{matrix}\right.\)

Vậy: S={1}

b) ĐKXĐ: \(x\notin\left\{3;-3\right\}\)

Ta có: \(\dfrac{5}{x-3}-\dfrac{2x-3}{x+3}=\dfrac{2x\left(1-x\right)}{x^2-9}\)

\(\Leftrightarrow\dfrac{5\left(x+3\right)}{\left(x-3\right)\left(x+3\right)}-\dfrac{\left(2x-3\right)\left(x-3\right)}{\left(x-3\right)\left(x+3\right)}=\dfrac{2x\left(1-x\right)}{\left(x-3\right)\left(x+3\right)}\)

Suy ra: \(5x+15-2x^2+6x+3x-9-2x+2x^2=0\)

\(\Leftrightarrow12x+6=0\)

\(\Leftrightarrow12x=-6\)

hay \(x=-\dfrac{1}{2}\)(thỏa ĐK)

Vậy: \(S=\left\{-\dfrac{1}{2}\right\}\)

`@` `\text {Ans}`

`\downarrow`

`a,`

`5.125.25 \div 5^6`

`=`\(5\cdot5^3\cdot5^2\div5^6\)

`=`\(5^{1+3+2-6}=5^{6-6}=5^0=1\) 

`b,`

\(2^{14}\div\left(2^6\cdot32\right)\)

`=`\(2^{14}\div\left(2^6\cdot2^5\right)\)

`=`\(2^{14}\div2^{11}=2^3\)

`c,`

`3.3^5\div 27`

`=`\(3\cdot3^5\div3^3\)

`=`\(3^{1+5-3}\)

`=`\(3^3\) 

`d,`

\(2^{15}\div\left(2^6\cdot32\right)=2^{15}\div\left(2^6\cdot2^5\right)=2^{15}\div2^{11}=2^4\)

`e,`

\(3^2\cdot27\div81=3^2\cdot3^3\div3^4=3\)

`g,`

\(100\cdot1000\cdot10000-10^9=10^2\cdot10^3\cdot10^4-10^9\)

`=`\(10^9-10^9=0\)

`h,`

\(125^4\div5^9=\left(5^3\right)^4\div5^9=5^{12}\div5^9=5^3\)

a) 1

b) 8

c) 27

d) 16

e) 3

g) 0

h) 125