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ĐK: ` x \ne 10; x \ne 0`
`120/(x-10)-3/5=120/x`
`<=>120/(x-10)-120/x=3/5`
`<=>1/(x-10) - 1/x= 1/200`
`<=> (x-x+10)/(x(x-10)) = 1/200`
`<=> 10/(x(x-10))= 1/200`
`<=> x^2-10=2000`
`<=>` \(\left[{}\begin{matrix}x=50\\x=-40\end{matrix}\right.\)
Vậy `S={50;-40}`.
`120/(x-10)-3/5=120/x(x ne 0,x ne 10)`
`<=>40/(x-10)-1/5=40/x`
`<=>200x-x(x-10)=200(x-10)`
`<=>200x-200x+2000-x^2+10x=0`
`<=>x^2-10x-2000=0`
`Delta'=25+2000=2025`
`<=>x_1=50,x_2=-40`
Vậy `S={50,-40}`
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\dfrac{120}{x}+\dfrac{120}{x-10}=\dfrac{3}{5}\left(dkxd:x>0,x\ne10\right)\)
\(\Leftrightarrow\dfrac{120}{x}+\dfrac{120}{x-10}-\dfrac{3}{5}=0\)
\(\Leftrightarrow\dfrac{120.5\left(x-10\right)+5.120x-3x\left(x-10\right)}{5x\left(x-10\right)}=0\)
\(\Leftrightarrow600x-6000+600x-3x^2+30x=0\)
\(\Leftrightarrow-3x^2+1230x-6000=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}x\approx405\\x\approx5\end{matrix}\right.\)\(\left(tmdk\right)\)
Vậy ...
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\sqrt{\left(120-11\right)^2}+\sqrt{\left(10-\sqrt{120}\right)^2}\)
\(=120-11+10+\sqrt{120}\)
\(=\sqrt{120}\left(\sqrt{120}+1\right)-1\)
\(a,=\left(120-11\right)+\left|10-\sqrt{120}\right|=109+\sqrt{120}-10=99+2\sqrt{30}\\ b,=\sqrt{\left(\sqrt{x+1}+1\right)^2-\left(\sqrt{x+1}+1\right)^2}=\sqrt{0}=0\)
![](https://rs.olm.vn/images/avt/0.png?1311)
17: \(x-\sqrt{x}-2=\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\)
18: \(x-3\sqrt{x}+2=\left(\sqrt{x}-1\right)\left(\sqrt{x}-2\right)\)
19: \(x\sqrt{x}-x+\sqrt{x}-1=\left(\sqrt{x}-1\right)\left(x+1\right)\)
20: \(x\sqrt{x}+y\sqrt{y}+x-y\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y\right)+\left(\sqrt{x}+\sqrt{y}\right)\left(\sqrt{x}-\sqrt{y}\right)\)
\(=\left(\sqrt{x}+\sqrt{y}\right)\left(x-\sqrt{xy}+y+\sqrt{x}-\sqrt{y}\right)\)
\(17,=\left(\sqrt{x}-2\right)\left(\sqrt{x}+1\right)\\ 18,=\left(\sqrt{x}-2\right)\left(\sqrt{x}-1\right)\\ 19,=\left(x+1\right)\left(\sqrt{x}-1\right)\\ 20,=???\)
bn xem lại đề câu 20 nha
tik mik nha
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left\{{}\begin{matrix}x-y=10\\\dfrac{120}{x}-\dfrac{120}{y}=0,4\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=10+y\\\dfrac{120}{10+y}-\dfrac{120}{y}=0,4\end{matrix}\right.\\ \Leftrightarrow\left\{{}\begin{matrix}x=10+y\\\dfrac{120y-1200-120y}{y\left(10+y\right)}=0,4\left(2\right)\end{matrix}\right.\)
\(\left(2\right)\Leftrightarrow-3000=y^2+10y\\ \Leftrightarrow y^2+10y+3000=0\\\Leftrightarrow y^2+10y+25=-2975\\ \Leftrightarrow\left(y+5\right)^2=-2975\left(vô\:lí\right)\)
\(\Rightarrow\)pt vô nghiệm
vậy hệ phương trình đã cho vô nghiệm
![](https://rs.olm.vn/images/avt/0.png?1311)
Câu 3 :
A = 7776 . 8 - 2.243. 64
A = 62208 - 31104
A = 31104
Câu 1 :
a) \(12^5=3^5.4^5\)
b) \(20^6=4^6.5^6\)
c) \(54^3=6^3.9^3\)
Câu 2 :
a) \(3.5^{55}=3.\left(5^5\right)^{11}\)
b) \(4.3^{816}=4.\left(3^{17}\right)^{48}\)
c) \(9.8.7^{6412}=9.8.\left(7^{28}\right)^{229}\)
x + x * 2,7 + x * 6,3 = 120
x * 1 + x * 27 + x * 63 = 120
x * ( 1 + 2,7 + 6,3 ) = 120
x * 10 = 120
x = 120 : 10
x = 12