tui ko bít

\(\dfrac{56x}{16y}= \dfrac{72,144\%}{27,856\%}\\ \Rightarrow\dfrac{x}{y} = \dfrac{72,144\%}{27,856\%} : \dfrac{56}{16} = 0,75 = \dfrac{3}{4}\)

Gọi công thức E là FexOy
=>M(FexOy)=56x+16y(g/mol)

có %Oxi=16y=15,6x+4,46y<=>11,54y=16x=>11,54y=15,6x=>xy=11,5415,6≈3/4

\(\frac{2x.56}{2,24}=\frac{2\left(56x+16y\right)}{3,2}\)

\(\Leftrightarrow\frac{112x}{2,24}=\frac{56x+16y}{1,6}\)

\(\Leftrightarrow50x=\frac{56x+16y}{1,6}\)

\(\Leftrightarrow80x=56x+16y\)

\(\Leftrightarrow24x=16y\)

\(\Leftrightarrow\frac{x}{y}=\frac{16}{24}=\frac{2}{3}\)

\(\Leftrightarrow x=2;y=3\)

Vậy .....................

a) ĐKXĐ : \(3\le x\le7\)

Ta có \(A=1.\sqrt{x-3}+1.\sqrt{7-x}\)

\(\le\sqrt{\left(1+1\right)\left(x-3+7-x\right)}=\sqrt{8}\)(BĐT Bunyacovski)

Dấu "=" xảy ra <=> \(\dfrac{1}{\sqrt{x-3}}=\dfrac{1}{\sqrt{7-x}}\Leftrightarrow x=5\)

\(1,\\ a,A\le\sqrt{\left(x-3+7-x\right)\left(1+1\right)}=\sqrt{8}=2\sqrt{2}\\ A^2=4+2\sqrt{\left(x-3\right)\left(7-x\right)}\ge4\Leftrightarrow A\ge2\\ \Leftrightarrow2\le A\le2\sqrt{2}\\ \left\{{}\begin{matrix}A_{min}\Leftrightarrow\left(x-3\right)\left(7-x\right)=0\Leftrightarrow...\\A_{max}\Leftrightarrow x-3=7-x\Leftrightarrow x=5\end{matrix}\right.\)

\(B=\dfrac{\dfrac{5}{2}\left(4x^4+4x^2+1\right)+2\left(x^4-x^2+\dfrac{1}{4}\right)}{\left(2x^2+1\right)^2}\\ B=\dfrac{\dfrac{5}{2}\left(2x^2+1\right)^2+2\left(x^2-\dfrac{1}{2}\right)^2}{\left(2x^2+1\right)^2}=\dfrac{5}{2}+\dfrac{2\left(x^2-\dfrac{1}{2}\right)^2}{\left(2x^2+1\right)^2}\ge\dfrac{5}{2}\)

\(B=\dfrac{3\left(4x^4+4x^2+1\right)-4x^2}{\left(1+2x^2\right)^2}=\dfrac{3\left(1+2x^2\right)^2-4x^2}{\left(1+2x^2\right)^2}=3-\dfrac{4x^2}{\left(1+2x^2\right)^2}\)

Vì \(-\dfrac{4x^2}{\left(1+2x^2\right)^2}\le0\Leftrightarrow B\le3\)

\(\Leftrightarrow\left\{{}\begin{matrix}B_{min}\Leftrightarrow x^2=\dfrac{1}{2}\Leftrightarrow x=\pm\dfrac{1}{\sqrt{2}}\\B_{max}\Leftrightarrow x=0\end{matrix}\right.\)

\(2,\)

Ta có \(\left(y-2x\right)^2=\left(-2x+y\right)^2=\left[\dfrac{1}{3}\left(-6x\right)+\dfrac{1}{4}\left(4y\right)\right]^2\)

\(\Leftrightarrow\left(y-2x\right)^2\le\left[\left(\dfrac{1}{3}\right)^2+\left(\dfrac{1}{4}\right)^2\right]\left[\left(-6x\right)^2+\left(4y\right)^2\right]=\dfrac{5^2}{3^2\cdot4^2}\left(36x^2+16y^2\right)=\dfrac{5^2}{4^2}\\ \Leftrightarrow\left|y-2x\right|\le\dfrac{5}{4}\\ \Leftrightarrow-\dfrac{5}{4}\le y-2x\le\dfrac{5}{4}\\ \Leftrightarrow\dfrac{15}{4}\le y-2x+5\le\dfrac{25}{4}\)

\(Max\Leftrightarrow\left\{{}\begin{matrix}-18x=16y\\y-2x=\dfrac{5}{4}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{2}{5}\\y=\dfrac{9}{20}\end{matrix}\right.\\ Min\Leftrightarrow\left\{{}\begin{matrix}-18x=16y\\y-2x=-\dfrac{5}{4}\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{2}{5}\\y=-\dfrac{9}{20}\end{matrix}\right.\)

bài nâng cao à bạn !!!!!!!!!

Ta có: x+3y=5 => x=5-3y 

Lại có: A=x^2+y^2+16y+2x

=> A=(5-3y)^2+y^2+16y+2(5-3y)=25-30y+9y^2+y^2+16y+10-6y

       =35+10y^2-20y=10(y^2-2y+1)+25=10(y-1)^2+25

Ta thấy: 10(y-1)^2 luôn lớn hơn hoặc bằng 0 với mọi y

=> A luôn lớn hơn hoặc bằng 25 với mọi y

Dấu "=" xảy ra <=> 10(y-1)^2=0 <=> y=1 => x=5-3*1=2

Vậy minA=25 <=> x=2; y=1