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HH
1
NL
Nguyễn Lê Phước Thịnh
CTVHS
15 tháng 4
Bài 5:
a: \(\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right)\)
\(=\frac{\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)+\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)-2x+1}{2x-1}\)
\(=\frac{x\sqrt2-\sqrt{x}+\sqrt{2x}-1+2x+\sqrt{2x}+x\sqrt2+\sqrt{x}-2x+1}{2x-1}\)
\(=\frac{2x\sqrt2+2\sqrt{2x}}{2x-1}\)
\(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\)
\(=\frac{2x-1+\left(\sqrt{x}+1\right)\left(\sqrt{2x}-1\right)-\left(\sqrt{2x}+\sqrt{x}\right)\left(\sqrt{2x}+1\right)}{2x-1}\)
\(=\frac{2x-1+x\sqrt2-\sqrt{x}+\sqrt{2x}-1-2x-\sqrt{2x}-x\sqrt2-\sqrt{x}}{2x-1}\)
\(=\frac{-2\sqrt{x}-2}{2x-1}\)
Ta có: \(P=\left(\frac{\sqrt{x}+1}{\sqrt{2x}+1}+\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}-1\right):\left(1+\frac{\sqrt{x}+1}{\sqrt{2x}+1}-\frac{\sqrt{2x}+\sqrt{x}}{\sqrt{2x}-1}\right)\)
\(=\frac{2x\sqrt2+2\sqrt{2x}}{2x-1}:\frac{-2\left(\sqrt{x}+1\right)}{2x-1}=\frac{2\sqrt{2x}\left(\sqrt{x}+1\right)}{-2\left(\sqrt{x}+1\right)}=-\sqrt{2x}\)
b: \(P=-\sqrt{2x}=-\sqrt{2\cdot\frac12\left(3+2\sqrt2\right)}\)
\(=-\sqrt{3+2\sqrt2}=-\sqrt{\left(\sqrt2+1\right)^2}=-\left(\sqrt2+1\right)=-\sqrt2-1\)
Bài 6:
a: \(\frac{x+2}{x\cdot\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\)
\(=\frac{x+2}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{1}{\sqrt{x}-1}\)
\(=\frac{x+2+\left(\sqrt{x}+1\right)\left(\sqrt{x}-1\right)-x-\sqrt{x}-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}\)
\(=\frac{-\sqrt{x}+1+x-1}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{\sqrt{x}\left(\sqrt{x}-1\right)}{\left(\sqrt{x}-1\right)\left(x+\sqrt{x}+1\right)}=\frac{\sqrt{x}}{x+\sqrt{x}+1}\)
Ta có: \(P=1:\left(\frac{x+2}{x\cdot\sqrt{x}-1}+\frac{\sqrt{x}+1}{x+\sqrt{x}+1}-\frac{\sqrt{x}+1}{x-1}\right)\)
\(=1:\frac{\sqrt{x}}{x+\sqrt{x}+1}=\frac{x+\sqrt{x}+1}{\sqrt{x}}\)
b: P-3=\(\frac{x+\sqrt{x}+1-3\sqrt{x}}{\sqrt{x}}=\frac{\left(\sqrt{x}-1\right)^2}{\sqrt{x}}>0\forall x\) thỏa mãn ĐKXĐ
=>P>3∀x thỏa mãn ĐKXĐ
21 tháng 12 2021
\(5,6=5,60=5,600=5,6000\)
\(34,56=34,560=34,5600=34,56000\)
\(35,08=35,080=35,0800=35,08000\)
\(8,900=8,90=8,9=8,9000\)
MG
24 tháng 2 2022
a, x x 5,8=19,72
x=19,72:5,8
x=3.4
b,x:5,6=34,5
x=34,5 x 5,6
x=193,2
9B
TN
1
HP
9 tháng 10 2021
Bài 5:
a. \(\sqrt{x^2+2x+1}=\sqrt{9x^2}\)
<=> \(\sqrt{\left(x+1\right)^2}=\sqrt{\left(3x\right)^2}\)
<=> \(\left|x+1\right|=\left|3x\right|\)
<=> \(\left[{}\begin{matrix}x+1=3x\\x+1=-3x\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=0,5\\x=-0,25\end{matrix}\right.\)
b. \(\sqrt{x^2-\dfrac{2}{5}x+\dfrac{1}{25}}=\sqrt{\left(2x+1\right)^2}\)
<=> \(\sqrt{\left(x-\dfrac{1}{5}\right)^2}=\sqrt{\left(2x+1\right)^2}\)
<=> \(\left|x-\dfrac{1}{5}\right|=\left|2x+1\right|\)
<=> \(\left[{}\begin{matrix}x-\dfrac{1}{5}=2x+1\\x-\dfrac{1}{5}=-2x-1\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=-1,2\\x=-\dfrac{4}{15}\end{matrix}\right.\)
c. \(\sqrt{25x^2}=\sqrt{x^4}\)
<=> \(\sqrt{\left(5x\right)^2}=\sqrt{\left(x^2\right)^2}\)
<=> \(\left|5x\right|=\left|x^2\right|\)
<=> \(\left[{}\begin{matrix}5x=x^2\\5x=-x^2\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}5x-x^2=0\\5x+x^2=0\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x\left(5-x\right)=0\\x\left(5+x\right)=0\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\\5-x=0\end{matrix}\right.\\\left[{}\begin{matrix}x=0\\5+x=0\end{matrix}\right.\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}\left[{}\begin{matrix}x=0\\x=5\end{matrix}\right.\\\left[{}\begin{matrix}x=0\\x=-5\end{matrix}\right.\end{matrix}\right.\)
<=> \(\left[{}\begin{matrix}x=0\\x=5\\x=-5\end{matrix}\right.\)
19 tháng 7 2021
5a.
Pt có 2 nghiệm pb lhi:
\(\Delta=9+4m>0\Leftrightarrow m>-\dfrac{9}{4}\)
b. Phương trình có 2 nghiệm khi:
\(\Delta=1+4\left(-2m+1\right)\ge0\Rightarrow m\le\dfrac{5}{8}\)
6.
a. Pt có 2 nghiệm khi:
\(\Delta'=1-\left(m+2\right)\ge0\Leftrightarrow m\le-1\)
19 tháng 7 2021
6b
Khi \(m\le-1\), theo hệ thức Viet ta có: \(\left\{{}\begin{matrix}x_1+x_2=2\\x_1x_2=m+2\end{matrix}\right.\)
\(x^2_1+x^2_2=10\Leftrightarrow\left(x_1+x_2\right)^2-2x_1x_2=10\)
\(\Leftrightarrow4-2\left(m+2\right)=10\)
\(\Leftrightarrow m=-5\)
B.
\(x^2_1+x_2^2+4x_1x_2=0\)
\(\Leftrightarrow\left(x_1+x_2\right)^2+2x_1x_2=0\)
\(\Leftrightarrow4+2\left(m+2\right)=0\)
\(\Leftrightarrow m=-4\)
25 tháng 4 2022
\(n_{hh}=\dfrac{5,6}{22,4}=0,25\left(mol\right)\)
PTHH:
CuO + H2 --to--> Cu + H2O
CuO + CO --to--> Cu + CO2
Theo pthh: nCuO = nhh = 0,25 (mol)
=> mCuO = 0,25.80 = 20 (g)
D
2
17 tháng 1 2022
Bài 5
\(n_{Al_2O_3}=\dfrac{10,2}{102}=0,1\left(mol\right)\)
\(n_{HCl}=\dfrac{18,25}{36,5}=0,5\left(mol\right)\)
PTHH: Al2O3 + 6HCl --> 2AlCl3 + 3H2O
Xét tỉ lệ: \(\dfrac{0,1}{1}>\dfrac{0,5}{6}\) => Al dư, HCl hết
PTHH: Al2O3 + 6HCl --> 2AlCl3 + 3H2O
\(\dfrac{1}{12}\)<----0,5------->\(\dfrac{1}{6}\)----->0,25
=> \(\left\{{}\begin{matrix}m_{Al\left(dư\right)}=10,2-\dfrac{1}{12}.102=1,7\left(g\right)\\m_{AlCl_3}=\dfrac{1}{6}.133,5=22,25\left(g\right)\\m_{H_2}=0,25.18=4,5\left(g\right)\end{matrix}\right.\)
Bài 6
a) \(n_{H_2}=\dfrac{2,24}{22,4}=0,1\left(mol\right)\)
\(n_{Mg}=\dfrac{4,8}{24}=0,2\left(mol\right)\)
PTHH: Mg + 2HCl --> MgCl2 + H2
0,1<-------------0,1<----0,1
=> \(n_{Mg\left(pư\right)}=0,1\left(mol\right)< 0,2\)
=> Mg dư => HCl hết
b) \(m_{MgCl_2}=0,1.95=9,5\left(g\right)\)
\(m_{Mg\left(dư\right)}=\left(0,2-0,1\right).24=2,4\left(g\right)\)
