Ta có \(\dfrac{1}{a^3\left(b+c\right)}=\dfrac{1}{\dfrac{1}{b^3c^3}\left(b+c\right)}=\dfrac{b^2c^2}{\dfrac{1}{b}+\dfrac{1}{c}}\)

Tương tự \(\Rightarrow VT=\dfrac{b^2c^2}{\dfrac{1}{b}+\dfrac{1}{c}}+\dfrac{c^2a^2}{\dfrac{1}{c}+\dfrac{1}{a}}+\dfrac{a^2b^2}{\dfrac{1}{a}+\dfrac{1}{b}}\)

\(\ge\dfrac{\left(ab+bc+ca\right)^2}{2\left(\dfrac{1}{a}+\dfrac{1}{b}+\dfrac{1}{c}\right)}\) (BĐT B.C.S)

\(=\dfrac{\left(ab+bc+ca\right)^2}{2\left(\dfrac{ab+bc+ca}{abc}\right)}\)

\(=\dfrac{ab+bc+ca}{2}\) (do \(abc=1\))

\(\ge\dfrac{3\sqrt[3]{abbcca}}{2}\)

\(=\dfrac{3\left(\sqrt[3]{abc}\right)^2}{2}=\dfrac{3}{2}\) (do \(abc=1\))

ĐTXR \(\Leftrightarrow a=b=c=1\)

Ta có:

\(a^3+b^3=3ab-1\)

\(\Leftrightarrow\left(a+b\right)\left(a^2-ab+b^2\right)=3ab-1\)

\(\Leftrightarrow\left(a+b\right)\left(a^2+2ab+b^2-3ab\right)=3ab-1\)

\(\Leftrightarrow\left(a+b\right)^3-3ab\left(a+b\right)=3ab-1\)

\(\Leftrightarrow\left(a+b\right)^3+1-3ab\left(a+b\right)-3ab=0\)

\(\Leftrightarrow\left(a+b+1\right)\left[a^2+2ab+b^2-a-b+1\right]-3ab\left(a+b+1\right)=0\)

\(\Leftrightarrow\left(a+b+1\right)\left(a^2+2ab+b^2-a-b+1-3ab\right)=0\)

\(\Leftrightarrow\left(a+b+1\right)\left(a^2-ab+b^2-a-b+1\right)=0\)

\(\Leftrightarrow\left(a+b+1\right)\left(2a^2+2b^2-2ab-2a-2b+2\right)=0\)

\(\Leftrightarrow\left(a+b+1\right)\left(a^2-2a+1+b^2-2b+1+a^2-2ab+b^2\right)=0\)

\(\Leftrightarrow\left(a+b+1\right)\left[\left(a-1\right)^2+\left(b-1\right)^2+\left(a-b^2\right)\right]=0\)

.......

Mình nghĩ đề a, b là 2 số dương nha, nếu a,b là 2 số dương thì mình loại được trường hợp a+b+1=0 nhé

R+HCln->RCln+H:

\(2R+2nHCl\rightarrow2RCl_n+nH_2\)

1. Gọi CTHH của oxit là N_xO_y.

Ta có: \(\dfrac{m_N}{m_O}=\dfrac{7}{20}\Rightarrow\dfrac{n_N}{n_O}=\dfrac{7}{20}:\dfrac{14}{16}=\dfrac{2}{5}\)

⇒ x:y = 2:5

→ N₂O₅

2. Gọi CTHH cần tìm là Fe_xO_y.

\(\Rightarrow\dfrac{m_{Fe}}{m_O}=\dfrac{7}{2}\Rightarrow\dfrac{n_{Fe}}{n_O}=\dfrac{7}{2}:\dfrac{56}{16}=1\)

⇒ x:y = 1

→ FeO

3. CTHH cần tìm: RO₂

Mà: %R = 46,7%
\(\Rightarrow\dfrac{M_R}{M_R+16.2}.100\%=46,7\%\)

⇒ M_R = 28 (g/mol)

→ SiO₂

tra loi đi

Ta có: 40n_NaOH + 56n_KOH = 3,04 (1)

PT: \(NaOH+HCl\rightarrow NaCl+H_2O\)

\(KOH+HCl\rightarrow KCl+H_2O\)

Theo PT: \(n_{NaCl}=n_{NaOH}\)

\(n_{KCl}=n_{KOH}\)

⇒ 58,5n_NaOH + 74,5n_KOH = 4,15 (2)

Từ (1) và (2) \(\Rightarrow\left\{{}\begin{matrix}n_{NaOH}=0,02\left(mol\right)\\n_{KOH}=0,04\left(mol\right)\end{matrix}\right.\)

\(\Rightarrow\%m_{KOH}=\dfrac{0,04.56}{3,04}.100\%\approx73,68\%\)

→ Đáp án: C

a

\(2x(x-y)-4y(y-x)\\=2x(x-y)-4y[-(x-y)]\\=2x(x-y)+4y(x-y)\\=(2x+4y)(x-y)\\=2(x+2y)(x-y)\)

đề đâu ạ?