\(3Fe+2O_2\rightarrow Fe_3O_4\)

                       0,15 mol

\(n_{Fe_3O_4}=\dfrac{m_{Fe_3O_4}}{M_{Fe_3O_4}}=\dfrac{34,8}{232}=0,15\left(mol\right)\)

\(\Rightarrow n_{Fe}=3n_{Fe_3O_4}=0,45\left(mol\right)\)

\(\Rightarrow m_{Fe}=n_{Fe}.M_{Fe}=0,45.56=25,2\left(g\right)\)

b) \(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a-b}{b}=\dfrac{b\left(k-1\right)}{b}=k-1\\\dfrac{c-d}{d}=\dfrac{d\left(k-1\right)}{d}=k-1\end{matrix}\right.\)\(\Rightarrow\dfrac{a-b}{b}=\dfrac{c-d}{d}\)

c) \(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a+b}{c+d}\Rightarrow\dfrac{a}{c}=\dfrac{a+b}{c+d}\Rightarrow\dfrac{a+b}{a}=\dfrac{c+d}{c}\)

d) \(\dfrac{a}{b}=\dfrac{c}{d}\Rightarrow\dfrac{a}{c}=\dfrac{b}{d}=\dfrac{a-b}{c-d}\Rightarrow\dfrac{a}{c}=\dfrac{a-b}{c-d}\Rightarrow\dfrac{a-b}{a}=\dfrac{c-d}{c}\)

a) \(\dfrac{a}{b}=\dfrac{c}{d}=k\Rightarrow\left\{{}\begin{matrix}a=bk\\c=dk\end{matrix}\right.\)

\(\Rightarrow\dfrac{a+b}{b}=\dfrac{bk+b}{b}=\dfrac{b\left(k+1\right)}{b}=k+1\) và \(\dfrac{c+d}{d}=\dfrac{dk+d}{d}=\dfrac{d\left(k+1\right)}{d}=k+1\)

\(\Rightarrow\dfrac{a+b}{b}=\dfrac{c+d}{d}\)

\(x^2+x-6=0\Leftrightarrow\left(x-2\right)\left(x+3\right)=0\Leftrightarrow\left[{}\begin{matrix}x-2=0\\x+3=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\\x=-3\end{matrix}\right.\)

\(2^{91}=\left(2^{13}\right)^7=8192^7\)

\(5^{35}=\left(5^5\right)^7=3125^7\)

Mà \(8192^7>3125^7\Rightarrow2^{91}>5^{35}\)

D

You wash yourself with soap and water in this shower.

3) \(C=\left(x-2\right)^2-\left(x-3\right)\left(x+3\right)=x^2-4x+4-x^2+9=-4x+13=-4.2+13=5\)4) \(D=\left(2x-3\right)^3+\left(4x+1\right)\left(16x^2-4x+1\right)=8x^3-36x^2+54x-27+64x^3-16x^2+4x+16x^2-4x+1=72x^3-36x^2+54x-26=72.\left(-2\right)^3-36.\left(-2\right)^2+54.\left(-2\right)-26=-854\)5)\(E=\left(3x+y\right)^3-\left(x+2y\right)\left(x^2-2xy+4y^2\right)=27x^3+27x^2y+9xy^2+y^3-x^3+2x^2y-4xy^2-2x^2y+4xy^2-8y^3=26x^3+27x^2y+9xy^2-7y^3=26.1^3+27.1^2.2+9.1.2^2-7.2^3=60\) \(\)

a) \(6x^3-6x=0\Leftrightarrow6x\left(x^2-1\right)=0\Leftrightarrow6x\left(x-1\right)\left(x+1\right)=0\Leftrightarrow\left[{}\begin{matrix}6x=0\\x-1=0\\x+1=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\\x=-1\end{matrix}\right.\)b) \(2x\left(3x+7\right)-6x^2=28\Leftrightarrow6x^2+14x-6x^2=28\Leftrightarrow14x=28\Leftrightarrow x=2\)

c) \(2\left(4x+4\right)-5\left(x-3\right)=0\Leftrightarrow8x+8-5x+15=0\Leftrightarrow3x=-23\Leftrightarrow x=-\dfrac{23}{3}\)