Tìm số nguyên x,y:
a) -2/x = y/3 và x<0<y
b) x-3/y-2 = 3/2 và x-y = 4
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a) \(3^{x+2}\cdot5^{y-3}=45^x\)
\(\Rightarrow3^{x+2}\cdot5^{y-3}=\left(3^2\right)^x\cdot5^x\)
\(\Rightarrow3^{x+2}\cdot5^{y-3}=3^{2x}\cdot5^x\)
\(\Rightarrow\left\{{}\begin{matrix}3^{x+2}=3^{2x}\\5^{y-3}=5^x\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x+2=2x\\y-3=x\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\\y-3=2\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=2\\y=5\end{matrix}\right.\)
Tìm y:
\(a,y+847\times2=1953-74\\ y+847\times2=1879\\ y+1694=1897\\ y=1897-1694\\ y=185\\ b,y:\left(7\times18\right)=5839+8591\\ y:126=14430\\ y=14430\times126\\ y=1818180.\)
\(a,y\times2,8+5,2\times y=48\\ y\times\left(2,8+5,2\right)=48\\ y\times8=48\\ y=\dfrac{48}{8}=6\\ ---\\ b,y\times12,25-y+y\times2,75=1050\\ y\times\left(12,25-1+2,75\right)=1050\\ y\times14=1050\\ y=\dfrac{1050}{14}=75\)
a: \(y\cdot2,8+y\cdot5,2=48\)
=>\(y\left(2,8+5,2\right)=48\)
=>\(8y=48\)
=>\(y=\dfrac{48}{8}=6\)
b: \(y\cdot12,25-y+y\cdot2,75=1050\)
=>\(y\left(12,25-1+2,75\right)=1050\)
=>\(y\cdot14=1050\)
=>\(y=\dfrac{1050}{14}=75\)
\(a,y\times27+y\times30+y\times44-y=10500\\\Rightarrow y\times\left(27+30+44-1\right)=10500\\ \Rightarrow y\times100=10500\\ \Rightarrow y=10500:100\\ \Rightarrow y=105\\ b,y\times285+115\times y=400\\ \Rightarrow y\times\left(285+115\right)=40\\ \Rightarrow y\times400=400\\ y=400:400\\ \Rightarrow y=1\)
\(a,\Rightarrow y\times\left(27+30+44-1\right)=10500\\ \Rightarrow y\times100=10500\\ \Rightarrow y=105\\ b,\Rightarrow y\times\left(285+115\right)=400\\ \Rightarrow y\times400=400\\ \Rightarrow y=1\)
Có: \(\left\{{}\begin{matrix}\left|x-3\right|\ge0\forall x\\\left|y-1\right|\ge0\forall y\end{matrix}\right.\)
\(\Rightarrow\left|x-3\right|+\left|y-1\right|\ge0\forall x;y\)
Mà: \(\left|x-3\right|+\left|y-1\right|=0\)
nên: \(\left\{{}\begin{matrix}x-3=0\\y-1=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=3\\y=1\end{matrix}\right.\)
a) (y + 5) x 2020 = 205 x 2020
(y + 5) x 2020 = 414100
y + 5 = 414100 : 2020 = 205
y = 205 - 5 = 200
a) y= 200
b) y-45600 = 1600 × 4 ×25
y-45600=160000
y= 114400
a) Ta có : \(\frac{-2}{x}=\frac{y}{3}\Leftrightarrow xy=-6\)
Vì x < 0 < y nên
b) Ta có : \(\frac{x-3}{y-2}=\frac{3}{2}\)
\(\Leftrightarrow2\left(x-3\right)=3\left(y-2\right)\)
\(\Leftrightarrow2x-6=3y-6\)
\(\Leftrightarrow2x=3y\)
Mà x - y = 4 => x = 4 + y,do đó \(2\left(4+y\right)=3y\)
=> 8 + 2y = 3y
=> 3y - 2y = 8
=> y = 8
Thay y = 8 vào x - y = 4 ta có :
x - 8 = 4 => x = 4 + 8 = 12
Vậy x = 12,y = 8