\(n^2=4\)

\(\Rightarrow\left[\begin{array}{l}n=2\\ n=-2\end{array}\right.\)

vậy n=2 hoặc n=-2

\(\frac{1+\frac14+\frac17+\frac{1}{10}+\cdots+\frac{1}{100}}{\frac{1}{1\cdot100}+\frac{1}{4\cdot97}+\cdots+\frac{1}{97\cdot4}+\frac{1}{100\cdot1}}\)

\(=\frac{1+\frac14+\frac17+\frac{1}{10}+\cdots+\frac{1}{100}}{\frac{1}{101}\cdot\left(\frac11+\frac{1}{100}\right)+\frac{1}{101}\cdot\left(\frac14+\frac{1}{97}\right)+\cdots+\frac{1}{101}\cdot\left(\frac{1}{97}+\frac14\right)+\frac{1}{101}\cdot\left(\frac{1}{100}+\frac11\right)}\)

\(=\frac{1+\frac14+\frac17+\frac{1}{10}+\cdots+\frac{1}{100}}{\frac{2}{101}\cdot\left(1+\frac14+\frac17+\frac{1}{10}+\cdots+\frac{1}{100}\right)}\)

\(=\frac{1}{\frac{2}{101}}=\frac{101}{2}\)

\(a.\left(x-3\right)\left(y+2\right)=7=1\cdot7=7\cdot1=\left(-1\right)\cdot\left(-7\right)=\left(-7\right)\cdot\left(-1\right)\)

\(\begin{cases}x-3=1\Rightarrow x=4\\ y+2=7\Rightarrow y=5\end{cases}\)

\(\begin{cases}x-3=7\Rightarrow x=10\\ y+2=1\Rightarrow y=-1\end{cases}\)

\(\begin{cases}x-3=-1\Rightarrow x=2\\ y+2=-7\Rightarrow y=-9\end{cases}\)

\(\begin{cases}x-3=-7\Rightarrow x=-4\\ y+2=-1\Rightarrow y=-3\end{cases}\)

vậy (x; y) = {(4; 5); (10; -1); (2; -9); (-4; -3)}

b) xy-2y+3x-6=3

(x-2)y+3(x-2) = 3

(x-2)(y+3)=3=3*1=1*3=(-3)*(-1)=(-1)*(-3)

\(\begin{cases}x-2=3\Rightarrow x=5\\ y+3=1\Rightarrow y=-2\end{cases}\)

\(\begin{cases}x-2=1\Rightarrow y=3\\ y+3=3\Rightarrow y=0\end{cases}\)

\(\begin{cases}x-2=-3\Rightarrow x=-1\\ y+3=-1\Rightarrow y=-4\end{cases}\)

\(\begin{cases}x-2=-1\Rightarrow x=1\\ y+3=-3\Rightarrow y=0\end{cases}\)

vậy (x; y) = {(5; -2); (3; 0); (-1; -4); (1; 0)}

c) xy-5y+5y-24=12

xy-24=12x

xy=36

các số nguyên sao cho xy=36, (x;y) rất nhiều ví dụ (1; 36); (2; 18); (3; 12); ...

đặt: \(\frac{x}{4}=\frac{2y}{5}=\frac{5z}{6}=k\)

\(\Rightarrow\begin{cases}x=4k\\ y=\frac{5k}{2}\\ z=\frac{6k}{5}\end{cases}\) (1)

thay (1) vào biểu thức \(x^2-3y^2+2z^2=325\) ta được:

\(\left(4k\right)^2-3\cdot\left(\frac{5k}{2}\right)^2+2\cdot\left(\frac{6k}{5}\right)^2=325\)

\(16k^2-\frac{75k^2}{4}_{}+\frac{72k^2}{25}=325\)

\(\frac{1600k^2}{100}-\frac{1875k^2}{100}+\frac{288k^2}{100}=325\)

\(\frac{13k^2}{100}=325\Rightarrow13k^2=32500\)

\(=>k^2=2500\Rightarrow k=\pm50\)

\(\left[\begin{array}{l}\begin{cases}x=4k=4\cdot50=200\\ y=\frac{5k}{2}=\frac{5\cdot50}{2}=125\\ z=\frac{6k}{5}=\frac{6\cdot50}{5}=60\end{cases}\\ \begin{cases}x=4k=4\cdot\left(-50\right)=-200\\ y=\frac{5k}{2}=\frac{5\cdot\left(-50\right)}{2}=-125\\ z=\frac{6k}{5}=\frac{6\cdot\left(-50\right)}{5}=-60\end{cases}\end{array}\right.\)

kết luận: \(\left(x;y;z\right)=\left[\begin{array}{l}\left(200;125;60\right)\\ \left(-200;-125;-60\right)\end{array}\right.\)

số mol khí NO2 là:

\(n_{NO2}=\frac{V_{NO2}}{24,79}=\frac{6,1975}{24,79}=0,25\left(mol\right)\)

khối lượng khí NO2 là:

\(m_{NO2}=n_{NO2}\cdot M_{NO2}=0,25\cdot46=11,5\left(g\right)\)

câu 1: \(\left(2x+y\right)^3-2\left(y-x\right)^3\)

\(=8x^3+12x^2y+6xy^2+y^3-\left(2y^3-6y^2x+6x^2y-2x^3\right)\)

\(=8x^3+12x^2y+6xy^2+y^3-2y^3+6y^2x-6x^2y+2x^3\)

\(=10x^3+\left(12x^2y-6x^2y\right)+\left(6xy^2+6y^2x\right)+\left(y^3-2y^3\right)\)

\(=10x^3+6x^2y+12xy^2-y^3\)

câu 2: \(\left(2x-3\right)^3-2x\left(2x+1\right)^2\)

\(=8x^3-36x^2+54x-27-\left(8x^3+8x^2+2x\right)\)

\(=\left(8x^3-8x^3\right)+\left(-36x^2-8x^2\right)+\left(54x-2x\right)-27\)

\(=-44x^2+52x-27\)

câu 3: \(\left(3x-1\right)^3-27x^2\left(x+1\right)\)

\(=27x^3-27x^2+9x-1-\left(27x^3+27x^2\right)\)

\(=\left(27x^3-27x^3\right)+\left(-27x^2-27x^2\right)+9x-1\)

\(=-54x^2+9x-1\)

câu 4: \(\left(2x+1\right)^3-8x\left(x-1\right)^2\)

\(=8x^3+12x^2+6x+1-\left(8x^3-16x^2+8x\right)\)

\(=28x^2-2x+1\)

câu a: 15 - (13 + x) - x = - (23 - 17)

15 - 13 - x - x = -23 + 17

2 - 2x = -6

-2x = -6 - 2

-2x = -8

x = (-8): (-2) = 4

vậy x = 4

câu b: x - (35 - x) = 43 - 48

x - 35 + x = -5

2x = -5 + 35

2x = 30

x = 30 : 2

x = 15

vậy x = 15

câu c: - (35 - x) - (37 - x) + x = 33

-35 + x - 37 + x + x = 33

3x = 33 + 37 + 35

3x = 105

x = 105 : 3 = 35

vậy x = 35

câu d: - (x - 6 + 85) - (x + 51) = -54

-x + 6 - 85 - x - 51 = -54

-2x = -54 - 6 + 85 + 51

-2x = 76

x = 76 : (-2) = -38

vậy x = -38

câu 1: \(\left(2x+y\right)^3-2\left(y-x\right)^3\)

\(=8x^3+12x^2y+6xy^2+y^3-\left(2y^3-6y^2x+6x^2y-2x^3\right)\)

\(=8x^3+12x^2y+6xy^2+y^3-2y^3+6y^2x-6x^2y+2x^3\)

\(=10x^3+\left(12x^2y-6x^2y\right)+\left(6xy^2+6y^2x\right)+\left(y^3-2y^3\right)\)

\(=10x^3+6x^2y+12xy^2-y^3\)

câu 2: \(\left(2x-3\right)^3-2x\left(2x+1\right)^2\)

\(=8x^3-36x^2+54x-27-\left(8x^3+8x^2+2x\right)\)

\(=\left(8x^3-8x^3\right)+\left(-36x^2-8x^2\right)+\left(54x-2x\right)-27\)

\(=-44x^2+52x-27\)

câu 3: \(\left(3x-1\right)^3-27x^2\left(x+1\right)\)

\(=27x^3-27x^2+9x-1-\left(27x^3+27x^2\right)\)

\(=\left(27x^3-27x^3\right)+\left(-27x^2-27x^2\right)+9x-1\)

\(=-54x^2+9x-1\)

câu 4: \(\left(2x+1\right)^3-8x\left(x-1\right)^2\)

\(=8x^3+12x^2+6x+1-\left(8x^3-16x^2+8x\right)\)

\(=28x^2-2x+1\)

\(6HNO_3+Fe_2O_3\to2Fe\left(NO_3\right)_3+3H_2O\)

\(CO_2+2NaOH\to Na_2CO_3+H_2O\)

\(FeO+H_2\to Fe+H_2O\)

\(BaO+H_2O\to Ba\left(OH\right)_2\)

câu a: barium oxide

câu b: sulfur dioxide

câu c: diphosphorus pentoxide

8 : (a - 1) + 12 : (a - 1) = 5

(8 + 12) : (a - 1) = 5

20 : (a - 1) = 5

a - 1 = 20 : 5

a - 1 = 4

a = 1 + 4

a = 5

vậy a = 5