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Có x . y = 7 . 1
x . y = 7
suy ra x hoặc y là ước của 7
mà ước của 7 = 1 , 7 , -1 , -7
suy ra x = 1 thì y = 7
x = -1 thì y = -7
x = 7 thì y = 1
x = -7 thì y = -1
ta có : 7.1 = xy
=> xy = 7 = 1.7 = (-1).(-7)
Vậy: (x,y) \(\varepsilon\) {(1,7);(7,1);(-1,-7);(-7,-1)
Ta có: -35=(-5).7=5.(-7)
=> TH1: 2x-1=-5 2y+1=7 TH2: 2x-1=5 2y+1=-7
2x=(-5)+1=-4 2y=7-1=6 2x=5+1=6 2y=(-7)-1=-8
x=(-4):2=-2 y=6:2=3 x=6:2=3 y=(-8):2=-4
TH3: 2x-1=-7 2y+1=5 TH4: 2x-1=7 2y+1=-5
2x=(-7)+1=-6 2y=5-1=4 2x=7+1=8 2y=(-5)-1=-6
x=(-6):2=-3 y=4:2=2 x=8:2=4 y=(-6):2=-3
Vậy x\(\in\){-3;-2;3;4}, y\(\in\){-4;-3;2;3}
a)
\(\left|x\right|-2\left|x\right|+3\left|x\right|=16+6\left|x\right|-19\)
\(\left|x\right|-2\left|x\right|+3\left|x\right|-6\left|x\right|=16-19\)
\(\left|x\right|.\left(1-2+3-6\right)=-3\)
\(\left|x\right|.\left(-4\right)=-3\)
\(\left|x\right|=\dfrac{3}{4}\)
\(\Rightarrow\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=\dfrac{3}{4}\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-\dfrac{3}{4}\\x=\dfrac{3}{4}\end{matrix}\right.\)
b,
2.(|x| - 5) - 15 = 9
\(2.\left(\left|x\right|-5\right)=9+15\)
\(2.\left(\left|x\right|-5\right)=24\)
\(\left|x\right|-5=24:2\)
\(\left|x\right|-5=12\)
\(\left|x\right|=12+5\)
\(\left|x\right|=17\)
\(\Rightarrow\left[{}\begin{matrix}x=-17\\x=17\end{matrix}\right.\)
Vậy \(\left[{}\begin{matrix}x=-17\\x=17\end{matrix}\right.\)
c,
|8 - 2x| + |4y - 16| = 0
\(\Rightarrow\left\{{}\begin{matrix}\left|8-2x\right|=0\\\left|4y-16\right|=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}8-2x=0\\4y-16=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}2x=8\\4y=16\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=4\\y=4\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=4\\y=4\end{matrix}\right.\)
d,
|x - 14| + |2y - x| = 0
\(\Rightarrow\left\{{}\begin{matrix}\left|x-14\right|=0\\\left|2y-x\right|=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x-14=0\\2y-x=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=14\\2y=x\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=14\\2y=14\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=14\\y=7\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=14\\y=7\end{matrix}\right.\)
2.Tìm x, y, z biết
a,
2.|3x| + |y + 3| + |z - y| = 0
\(\Rightarrow\left\{{}\begin{matrix}2.\left|3x\right|=0\\\left|y+3\right|=0\\\left|z-y\right|=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}\left|3x\right|=0\\y+3=0\\z-y=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}3x=0\\y=-3\\z=y\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=0\\y=-3\\z=-3\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=0\\y=-3\\z=-3\end{matrix}\right.\)
b, (x - 3y)2 + | y + 4|= 0
\(\Rightarrow\left\{{}\begin{matrix}\left(x-3y\right)2=0\\\left|y+4\right|=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x-3y=0\\y+4=0\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=3y\\y=-4\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=3.\left(-4\right)\\y=-4\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}x=-12\\y=-4\end{matrix}\right.\)
Vậy \(\left\{{}\begin{matrix}x=-12\\y=-4\end{matrix}\right.\)
Đặt \(A=\frac{x^2+2x-1}{x-1}\)
Ta có:\(A=\frac{x^2+2x-1}{x-1}=\frac{\left(x-1\right)^2}{x-1}=x-1\)
Vậy để A nguyên thì x thỏa mãn mõi số nguyên
\(\hept{\begin{cases}x+y+z+t=1\\x+y+z=2\end{cases}}\)
\(\Rightarrow\left(x+y+z+t\right)-\left(x+y+z\right)=1-2\)
\(\Rightarrow t=-1\)
\(\hept{\begin{cases}x+y+z+t=1\\y+z+t=3\end{cases}}\)
\(\Rightarrow\left(x+y+z+t\right)-\left(y+z+t\right)=1-3\)
\(\Rightarrow x=-2\)
\(\hept{\begin{cases}x+y+z+t=1\\z+x+t=4\end{cases}}\)
\(\Rightarrow\left(x+y+z+t\right)-\left(z+x+t\right)=1-4\)
\(\Rightarrow y=-3\)
\(x+y+z+t=1\)
\(\Rightarrow\left(-2\right)+\left(-3\right)+\left(-1\right)+t=1\)
\(\Rightarrow\left(-6\right)+t=1\)
\(\Rightarrow t=7\)
\(\hept{\begin{cases}x+y=3\\y+z=-1\\z+x=-2\end{cases}}\)
\(\Rightarrow\left(x+y\right)+\left(y+z\right)+\left(z+x\right)=0\)
\(\Rightarrow2\left(x+y+z\right)=0\)
\(\Rightarrow x+y+z=0\)
\(\hept{\begin{cases}z=0-\left(x+y\right)=-3\\x=0-\left(y+z\right)=1\\y=0-\left(z+x\right)=2\end{cases}}\)
\(x = {-b \pm \sqrt{b^2-4ac} \over 2a}\)