Do vai trò của 3 biến là như nhau, không mất tính tổng quát giả sử \(x>y>z\)

Ta có: \(x-z=\left(x-y\right)+\left(y-z\right)\)

Đặt \(\left\{{}\begin{matrix}x-y=a>0\\y-z=b>0\end{matrix}\right.\)  

Do \(x;z\in\left[0;2\right]\Rightarrow x-z\le2\) hay \(a+b\le2\)

Ta có:

\(P=\dfrac{1}{a^2}+\dfrac{1}{b^2}+\dfrac{1}{\left(a+b\right)^2}\ge\dfrac{1}{2}\left(\dfrac{1}{a}+\dfrac{1}{b}\right)^2+\dfrac{1}{\left(a+b\right)^2}\ge\dfrac{1}{2}\left(\dfrac{4}{a+b}\right)^2+\dfrac{1}{\left(a+b\right)^2}\)

\(P\ge\dfrac{9}{\left(a+b\right)^2}\ge\dfrac{9}{2^2}=\dfrac{9}{4}\)

Dấu "=" xảy ra khi \(\left\{{}\begin{matrix}a=b\\a+b=2\\\end{matrix}\right.\) \(\Rightarrow a=b=1\) hay \(\left(x;y;z\right)=\left(0;1;2\right)\) và các hoán vị

Câu 2.

Nhiệt lượng bếp tỏa ra trong thời gian \(t=3min=180s\) là:

\(Q=UIt=RI^2t=60\cdot2,5^2\cdot180=675000J\)

Câu 3.

\(I_{Đ1}=\dfrac{U_{Đ1}}{R_{Đ1}}=\dfrac{6}{6}=1A\)

\(I_{Đ2}=\dfrac{U_{Đ2}}{R_{Đ2}}=\dfrac{1,5}{8}=\dfrac{3}{16}A\)

\(I_b=I_{Đ1}-I_{Đ2}=1-\dfrac{3}{16}=\dfrac{13}{16}A\)

\(R_b=\dfrac{U_b}{I_b}=\dfrac{1,5}{\dfrac{13}{16}}=\dfrac{24}{13}\Omega\)

nO2 = 5,6/22,4 = 0,25 (mol)

PTHH: 2KClO3 -> (t°, MnO2) 2KCl + 3O2

nKClO3 = 0,25 : 3 . 2 = 1/6 (mol)

nKClO3 = 1/6 . 122,5 = 245/12 (g)

nMg = 2,4/24 = 0,1 (mol)

PTHH: 2Mg + O2 -> (t°) 2MgO

LTL: 0,1/2 < 0,25 => O2 dư

nMgO = 0,1 (mol)

nMgO = 0,1 . 40 = 4 (g)

nO2 = 5,6 : 22,4 = 0,25(mol) 
pthh : 2KClO3 -t--> 2KCl + 3O2
           1/6     <----------------0,25(mol)
=>mKClO3 = 1/6.114,5=229/12(g)

nMg=2,4:24=0,1(mol)
pthh 2Mg+O2 -t-> 2MgO
               0,1--------->0,1(mol) 
=> mMgO = 0,1.40=4 (g) 

nO2 = 5,6/22,4 = 0,25 (mol)

PTHH: 2KClO3 -> (t°, MnO2) 2KCl + 3O2

nKClO3 = 0,25 : 3 . 2 = 1/6 (mol)

nKClO3 = 1/6 . 122,5 = 245/12 (g)

nMg = 2,4/24 = 0,1 (mol)

PTHH: 2Mg + O2 -> (t°) 2MgO

LTL: 0,1/2 < 0,25 => O2 dư

nMgO = 0,1 (mol)

nMgO = 0,1 . 40 = 4 (g)

a) \(\dfrac{A}{x-2}=\dfrac{x^2+3x+2}{x^2-4}\)

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

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

b) \(\dfrac{M}{x-1}=\dfrac{x^2+3x+2}{x+1}\)

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

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

a: Xét tứ giác OBAC có 

\(\widehat{OBA}+\widehat{OCA}=180^0\)

Do đó: OBAC là tứ giác nội tiếp

good

good->better

good => better