\(\left(1\right)C+O_2\xrightarrow[]{t^0}CO_2\\ \left(3\right)CO_2+Na_2O\rightarrow Na_2CO_3\\ \left(3\right)Na_2CO_3+CaCl_2\rightarrow CaCO_3+2NaCl\)

MP = 5cm.

\(a.Fe+2HCl\rightarrow FeCl_2+H_2\\ b.H_2SO_4+2NaOH\rightarrow Na_2SO_4+2H_2O\)

1)

\(\dfrac{x-1}{2014}+\dfrac{x-2}{2013}+\dfrac{x-3}{2012}+...+\dfrac{x-2014}{1}=2014\)

\(\Leftrightarrow\left(\dfrac{x-1}{2014}-1\right)+\left(\dfrac{x-2}{2013}-1\right)+...+\left(\dfrac{x-2014}{1}-1\right)=0\)

\(\Leftrightarrow\dfrac{x-2015}{2014}+\dfrac{x-2015}{2013}+...+\dfrac{x-2015}{1}=0\)

\(\Leftrightarrow\left(x-2025\right)\left(\dfrac{1}{2014}+\dfrac{1}{2013}+...+\dfrac{1}{1}\right)=0\)

\(\Leftrightarrow x=2015\)

Vậy \(S=\left\{2015\right\}\)

Lời giải:
$A=a^2+ab+b^2-3b-3a+3$

$4A=4a^2+4ab+4b^2-12a-12b+12$

$=(4a^2+4ab+b^2)-12a-12b+3b^2+12$

$=(2a+b)^2-6(2a+b)+9+(3b^2-6b+3)$

$=(2a+b-3)^2+3(b-1)^2\geq 0+3.0=0$

Vậy $A_{\min}=0$. Giá trị này đạt tại $2a+b-3=b-1=0$

$\Leftrightarrow b=1; a=1$

Câu B tương tự câu A nhé. Chỉ khác mỗi đặt tên biến.

---------------

$C=x^2+5y^2-4xy+2y-3$

$=(x^2-4xy+4y^2)+(y^2+2y)-3$

$=(x-2y)^2+(y^2+2y+1)-4$

$=(x-2y)^2+(y+1)^2-4\geq 0+0-4=-4$

Vậy $C_{\min}=-4$. Giá trị này đạt tại $x-2y=y+1=0$

$\Leftrightarrow y=-1; x=-2$

29 A => many

30 B => reading

31 I am fond of using Facebook in my free time

32 If we do more exercise, we will have good health

Lời giải:

$x^3+y^3=(x+y)^3-3xy(x+y)=2^3-3xy.2=8-6xy$

$=8-3.2xy=8-3[(x+y)^2-(x^2+y^2)]=8-3(2^2-34)=98$

----------------

$x^4+y^4=(x^2+y^2)^2-2x^2y^2=34^2-\frac{1}{2}(2xy)^2$

$=34^2-\frac{1}{2}[(x+y)^2-(x^2+y^2)]^2=34^2-\frac{1}{2}(2^2-34)^2=706$

Đề sai, em xem lại đề nhé