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mk biết có mỗi cách thôi, làm xằng vậy =))
Ta có :
\(5x=3y\)
\(\Leftrightarrow\dfrac{x}{3}=\dfrac{y}{5}\)
Đặt :
\(\dfrac{x}{3}=\dfrac{y}{5}=k\) \(\Leftrightarrow\left\{{}\begin{matrix}x=3k\\y=5k\end{matrix}\right.\)\(\left(1\right)\)
Thay \(\left(1\right)\) vào \(xy=375\) ta có :
\(3k.5k=375\)
\(\Leftrightarrow15k^2=375\)
\(\Leftrightarrow\left[{}\begin{matrix}k=25\\k=-25\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}k=5\\k=-5\end{matrix}\right.\)
+) \(k=5\Leftrightarrow\left[{}\begin{matrix}x=3.5=15\\y=5.5=25\end{matrix}\right.\)
+) \(k=-5\Leftrightarrow\left[{}\begin{matrix}x=3.\left(-5\right)=-15\\y=5\left(-5\right)=-25\end{matrix}\right.\)
Vậy ..
1 Cách nhé
\(5x=3y\Leftrightarrow\dfrac{x}{3}=\dfrac{y}{5}\)
Đặt : \(\dfrac{x}{3}=\dfrac{y}{5}=k\)
Ta có : \(\dfrac{x}{3}=k\Leftrightarrow x=3k\)
\(\dfrac{y}{5}=k\Leftrightarrow y=5k\)
Mà : \(3k.5k=375\)
\(\Leftrightarrow15k^2=375\)
\(\Leftrightarrow k^2=25\)
\(\Leftrightarrow\left[{}\begin{matrix}k=5\\k=-5\end{matrix}\right.\)
Khi \(k=5\), thì : \(\left\{{}\begin{matrix}x=15\\y=25\end{matrix}\right.\)
Khi \(k=-5,\) thì : \(\left\{{}\begin{matrix}x=-15\\y=-25\end{matrix}\right.\)
Vậy ..........
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\left(5x-1\right)^2+2\left(1-5x\right)\left(4+5x\right)+\left(5x+4\right)^2\)
\(=\left(5x-1\right)^2-2\left(5x-1\right)\left(5x+4\right)+\left(5x+4\right)^2\)
\(=\left[\left(5x-1\right)-\left(5x+4\right)\right]^2\)
\(=\left(5x-1-5x-4\right)^2\)
\(=\left(-5\right)^2\)
\(=25\)
![](https://rs.olm.vn/images/avt/0.png?1311)
(5x-1)^2+2(5x-1)(5x+1)+5(2x-1)
=25x^2-10x+1+2(25x^2-1)+10x-5
=25x^2-4+50x^2-2
=75x^2-6
\(\left(5x-1\right)^2+2\left(5x-1\right)\left(5x+1\right)+5\left(2x-1\right)\)
\(=25x^2-10x+1+2\left(25x^2-1\right)+10x-5\)
\(=25x^2-10x+1+50x^2-2+10x-5\)
\(=\left(25x^2+50x^2\right)+\left(10x-10x\right)+\left(1-2-5\right)\)
\(=75x^2-6\)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(\Rightarrow5^x\left(1+5+5^2\right)=3875\\ \Rightarrow5^x=\dfrac{3875}{31}=125=5^3\\ \Rightarrow x=3\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a, \(-4x+5+2x-1=3\Leftrightarrow-2x=-1\Leftrightarrow x=\dfrac{1}{2}\)
b, \(-2x+2=2\Leftrightarrow x=0\)
c, \(-2x-6=-8\Leftrightarrow x=1\)
![](https://rs.olm.vn/images/avt/0.png?1311)
a: \(=2x^3:\dfrac{-3}{2}x+4x:\dfrac{3}{2}x-5:\dfrac{3}{2}\)
=-4/3x^2+8/3-10/3
=-4/3x^2-2/3
d: \(\dfrac{3x^3-5x+2}{x-3}=\dfrac{3x^3-9x^2+9x^2-27x+22x-66+68}{x-3}\)
\(=3x^2+9x+22+\dfrac{68}{x-3}\)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
![](https://rs.olm.vn/images/avt/0.png?1311)
\(C=x^4\left(x-4\right)-x^3\left(x-4\right)+x^2\left(x-4\right)-x\left(x-4\right)+x-1\)
\(C=\left(x-4\right)\left(x^4-x^3+x^2-x\right)+\left(x-1\right)=\left(4-4\right)\left(4^4-4^3+4^2-4\right)+\left(4-1\right)=3\)
\(5^{x+1}-2.5^x=375\Rightarrow5^x.5-2.5^x=375\Rightarrow3.5^x=375\Rightarrow5^x=125=5^3\Rightarrow x=3\)
5x.5-2.5x=375
5x. (5-2)=375
5x=125
x=3