Áp dụng BĐT Bunhiacopxki (cho tất cả các bài):

1.

\(\left(3x+4y\right)^2\le\left(3^2+4^2\right)\left(x^2+y^2\right)=25\)

\(\Rightarrow\left|3x+4y\right|\le5\)

Dấu "=" xảy ra khi \(\left(x;y\right)=\left(\dfrac{3}{5};\dfrac{4}{5}\right)\)

2.

\(\left(x+2y\right)^2=\left(1.x+\sqrt{2}.\sqrt{2y}\right)^2\le\left(1+2\right)\left(x^2+2y^2\right)=3\)

\(\Rightarrow\left|x+2y\right|\le\sqrt{3}\)

Dấu "=" xảy ra khi \(\left(x;y\right)=\left(\dfrac{1}{\sqrt{3}};\dfrac{1}{\sqrt{3}}\right)\)

4.

a.

Áp dụng Bunhiacopxki:

\(\left(b+c+c+a+a+b\right)\left(\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}\right)\ge\left(a+b+c\right)^2\)

\(\Rightarrow2\left(a+b+c\right)\left(\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}\right)\ge\left(a+b+c\right)^2\)

\(\Rightarrow\dfrac{a^2}{b+c}+\dfrac{b^2}{c+a}+\dfrac{c^2}{a+b}\ge\dfrac{a+b+c}{2}\)

Dấu "=" xảy ra khi \(a=b=c\)

3.

Từ giả thiết:

\(x^2+y^2+z^2-2x-4y+2z=3\)

\(\Leftrightarrow\left(x-1\right)^2+\left(y-2\right)^2+\left(z+1\right)^2=9\)

Ta có:

\(\left|x+2y+2z-20\right|=\left|x-1+2\left(y-2\right)+2\left(z+1\right)-17\right|\)

\(\Rightarrow\left|x+2y+2z-20\right|\le\left|x-1+2\left(y-2\right)+2\left(z+1\right)\right|+17\)

Lại có:

\(\left[\left(x-1\right)+2\left(y-2\right)+2\left(z+1\right)\right]^2\le\left(1+4+4\right)\left[\left(x-1\right)^2+\left(y-2\right)^2+\left(z+1\right)^2\right]=81\)

\(\Rightarrow\left|x-1+2\left(y-2\right)+2\left(z+1\right)\right|\le9\)

\(\Rightarrow\left|x+2y+2z-20\right|\le9+17=26\)

\(\Rightarrow A_{max}=26\) khi \(\left(x;y;z\right)=\left(0;0;-3\right)\)

\(ZnO,BaO,K_2O\)

\(ZnCl_2,BaCl_2,KCl\)

\(Zn\left(OH\right)_2,Ba\left(OH\right)_2,KOH\)

\(ZnSO_4,BaSO_4,K_2SO_4\)

\(Zn\left(NO_3\right)_2,Ba\left(NO_3\right)_2,KNO_3\)

\(ZnCO_3,BaCO_3,K_2CO_3\)

\(Zn_3\left(PO_4\right)_2,Ba_3\left(PO_4\right)_2,K_3PO_4\)

\(\Leftrightarrow3^{x-3}=27\)

=>x-3=3

hay x=6

mail mình là:

hoangclgt2003@gmail.com

quynhphamtrinh@gmail.com

Câu bữa trc mình gửi á

Câu 6)

\(U_{13}=U_{12}+U_{23}=2,4+2,5=4,9V\\ U_{23}=U_{13}-U_{12}=5,4V\\ U_{12}=U_{13}-U_{23}=11,7V\) 

Câu 7)

\(I_1=I_2=0,25A\\ I_3=I-I_1\left(I_2\right)=0,1A\\ U=U_1=U_3=9V\\ U_2=U-U_1=3V\)

Bổ sung bài 5)

Số chỉ A₂ là 0,35A

\(I=I_1=I_2=0,35A\)

 1/x + 1/y = 1/2 
<=> 2/x + 2/y =1 
<=> 2x + 2y = xy 
<=> xy - 2x - 2y+4 =4 
<=> (x-2).(y-2) =4 
ta có các cặp (2;2),(-2;-2),(1;4), (-1;-4) 
sau đó thử từng cặp một bạn nhé

cảm ơn bạn Thắng Hoàng nhưng có cái này mình ko hiểu lắm mấu chứa ẩn thì làm sao mà khử dc