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b:
=>x(y-3)+3(y-3)=17
=>(y-3)(x+3)=17
\(\Leftrightarrow\left(x+3,y-3\right)\in\left\{\left(1;17\right);\left(17;1\right);\left(-1;-17\right);\left(-17;-1\right)\right\}\)
hay \(\left(x,y\right)\in\left\{\left(-2;20\right);\left(14;4\right);\left(-4;-14\right);\left(-20;2\right)\right\}\)
a: =>x(2y+3)+2(2y+3)=5
=>(2y+3)(x+2)=5
\(\Leftrightarrow\left(2y+3;x+2\right)\in\left\{\left(1;5\right);\left(-1;-5\right);\left(5;1\right);\left(-5;-1\right)\right\}\)
hay \(\left(y,x\right)\in\left\{\left(-1;3\right);\left(-2;-7\right);\left(1;-1\right);\left(-4;-3\right)\right\}\)
\(\left(x+2\right)-2=0\)
\(\Rightarrow x+2-2=0\)
\(\Rightarrow x=0\)
\(\left(x+3\right)+1=7\)
\(\Rightarrow x+3+1=7\)
\(\Rightarrow x+4=7\)
\(\Rightarrow x=3\)
\(\left(3x-4\right)+4=12\)
\(\Rightarrow3x-4+4=12\)
\(\Rightarrow3x=12\)
\(\Rightarrow x=4\)
\(\left(5x+4\right)-1=13\)
\(\Rightarrow5x+4-1=13\)
\(\Rightarrow5x+3=13\)
\(\Rightarrow5x=10\)
\(\Rightarrow x=2\)
\(\left(4x-8\right)-3=5\)
\(\Rightarrow4x-8-3=5\)
\(\Rightarrow4x-11=5\)
\(\Rightarrow4x=16\)
\(\Rightarrow x=4\)
\(8-\left(2x+4\right)=2\)
\(\Rightarrow8-2x-4=2\)
\(\Rightarrow4-2x=2\)
\(\Rightarrow2x=2\)
\(\Rightarrow x=1\)
\(7+\left(5x+2\right)=14\)
\(\Rightarrow7+5x+2=14\)
\(\Rightarrow9+5x=14\)
\(\Rightarrow5x=5\)
\(\Rightarrow x=1\)
\(5-\left(3x-11\right)=1\)
\(\Rightarrow5-3x+11=1\)
\(\Rightarrow16-3x=1\)
\(\Rightarrow3x=15\)
\(\Rightarrow x=5\)
\(\left(2+2x\right)\left(y+5\right)=0\)
\(\Rightarrow\orbr{\begin{cases}2+2x=0\\y+5=0\end{cases}}\)
\(\Rightarrow\orbr{\begin{cases}x=-1\\y=-5\end{cases}}\)
\(2xy+x+2y=13\\ \Rightarrow2xy+x+2y+1-1=13\\ \Rightarrow\left(2xy+2y\right)+\left(x+1\right)=13+1\\ \Rightarrow2y\left(x+1\right)+\left(x+1\right)=14\\ \Rightarrow\left(x+1\right)\left(2y+1\right)=14\\ \Rightarrow\left(x+1\right);\left(2y+1\right)\inƯ\left(14\right)\\ \Rightarrow\left(x+1\right);\left(2y+1\right)\in\left\{-14;-7;-2;-1;1;2;7;14\right\}\)
\(x+1\) | \(-14\) | \(-7\) | \(-2\) | \(-1\) | \(1\) | \(2\) | \(7\) | \(14\) |
\(2y+1\) | \(-1\) | \(-2\) | \(-7\) | \(-14\) | \(14\) | \(7\) | \(2\) | \(1\) |
\(x\) | \(-15\) | \(-8\) | \(-3\) | \(-2\) | \(0\) | \(1\) | \(6\) | \(13\) |
\(y\) | \(-1\) | \(-\dfrac{3}{2}\) | \(-4\) | \(-\dfrac{15}{2}\) | \(\dfrac{13}{2}\) | \(3\) | \(\dfrac{1}{2}\) | \(0\) |
Vì \(x,y\in N\Rightarrow\left(x;y\right)=\left(0;\dfrac{13}{2}\right),\left(1;3\right),\left(6;\dfrac{1}{2}\right),\left(13;0\right)\)
Vậy \(\left(x;y\right)=\left(0;\dfrac{13}{2}\right),\left(1;3\right),\left(6;\dfrac{1}{2}\right),\left(13;0\right)\)
ta có 12 = 12.1=2.6=3.4=>
(x-1).(2y + 3) = 12.1=2.6=3.4
nếu x - 1 =1 2y + 3 = 12
x = 1 +1 2y = 12-3
x = 2 2y = 9
y = 9 : 2
vì x;y thuộc N* nên trường hợp này loại [....]
(rồi bạn cứ thử với các trường hợp khác là xong nha )
Chúc bạn học tốt !
2xy-5x+2y-14=0
=>2xy+2y-5x-5-9=0
=>2y(x+1)-5(x+1)=9
=>(x+1)(2y-5)=9
=>\(\left(x+1\right)\left(2y-5\right)=1\cdot9=\left(-1\right)\cdot\left(-9\right)=\left(-9\right)\cdot\left(-1\right)=9\cdot1=3\cdot3=\left(-3\right)\cdot\left(-3\right)\)
=>\(\left(x+1;2y-5\right)\in\left\{\left(1;9\right);\left(-1;-9\right);\left(-9;-1\right);\left(9;1\right);\left(3;3\right);\left(-3;-3\right)\right\}\)
=>\(\left(x;y\right)\in\left\{\left(0;7\right);\left(-2;-2\right);\left(-10;2\right);\left(8;3\right);\left(2;4\right);\left(-4;1\right)\right\}\)