xy+12=x-y
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\(\left|x+1\right|+\left|x-5\right|=3x+1\left(đk:x\ge-\dfrac{1}{3}\right)\)
\(\Leftrightarrow x+1+\left|x-5\right|=3x+1\)
\(\Leftrightarrow\left|x-5\right|=2x\)
\(\Leftrightarrow\left[{}\begin{matrix}x-5=2x\left(x\ge5\right)\\x-5=-2x\left(-\dfrac{1}{3}\le x< 5\right)\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=-5\left(ktm\right)\\x=\dfrac{5}{3}\left(tm\right)\end{matrix}\right.\)
\(\Rightarrow\left[{}\begin{matrix}-x-1+5-x=3x+1\left(x< -1\right)\\x+1+5-x=3x+1\left(-1\le x< 5\right)\\x+1+x-5=3x+1\left(x\ge5\right)\end{matrix}\right.\\ \Rightarrow\left[{}\begin{matrix}x=\dfrac{3}{5}\left(ktm\right)\\x=\dfrac{5}{3}\left(tm\right)\\x=-5\left(ktm\right)\end{matrix}\right.\Rightarrow x=\dfrac{5}{3}\)
Ta có : \(\frac{x}{y}=\frac{11}{7}\Leftrightarrow\frac{x}{11}=\frac{y}{7}\)
Áp dụng TC của dãy tỉ số bằng nhau ta có:
\(\frac{x}{11}=\frac{y}{7}=\frac{x-y}{11-7}=\frac{12}{4}=3\)
\(\Rightarrow\hept{\begin{cases}x=3.11=33\\y=3.7=21\end{cases}}\)
a) \(\frac{x^2-xy-x+y}{x^2+xy-x-y}\)=\(\frac{x\left(x-y\right)-\left(x-y\right)}{x\left(x+y\right)-\left(x+y\right)}\)=\(\frac{\left(x-1\right)\left(x-y\right)}{\left(x-1\right)\left(x+y\right)}\)=\(\frac{x-y}{x+y}\)
b) \(\frac{x^2-xy}{5y^2-5xy}\)=\(\frac{x\left(x-y\right)}{-5y\left(x-y\right)}\)=\(\frac{-x}{5y}\)
c) \(\frac{3x^2-12x+12}{x^4-8x}\)=\(\frac{3\left(x^2-4x+4\right)}{x\left(x^3-2^3\right)}\)=\(\frac{3\left(x-2\right)^2}{x\left(x-2\right)\left(x^2+2x+4\right)}\)=\(\frac{3\left(x-2\right)}{x\left(x^2+2x+4\right)}\)
(1+9)+(2+8)+(3+7)+(4+6)+5 x (2+8)+(3+7)+(4+6)+5=10+10+10+10+10+10+10+(5+5)
=10+10+10+10+10+10+10+10=80
Chu vi bánh xe đó là:
1,9 x 3, 14 = 5,966 ( m)
Ctrl + W là nút mở tab mới, mình bấm rồi.
1)
xy + x - 4y = 12
x + y(x - 4) = 12
y(x - 4) = 12 - x
\(y=\dfrac{-x+12}{x-4}\)
Vì \(x,y\inℕ\) nên
\(\left(-x+12\right)⋮\left(x-4\right)\)
\(\left(-x+12\right)-\left(x-4\right)⋮\left(x-4\right)\)
\(16⋮\left(x-4\right)\)
\(\left(x-4\right)\inƯ\left(16\right)\)
\(\left(x-4\right)\in\left\{1;-1;2;-2;4;-4;8;-8;16;-16\right\}\)
\(x\in\left\{5;3;6;2;8;0;12;-4;20;-12\right\}\)
\(y\in\left\{\dfrac{-5+12}{5-4};\dfrac{-3+12}{3-4};\dfrac{-6+12}{6-4};\dfrac{-2+12}{2-4};\dfrac{-8+12}{8-4};\dfrac{-0+12}{0-4};\dfrac{-12+12}{12-4};\dfrac{4+12}{-4-4};\dfrac{-20+12}{20-4};\dfrac{12+12}{-12-4}\right\}\)
\(y\in\left\{7;-9;3;-5;1;-3;0;-2;-\dfrac{1}{2};-\dfrac{7}{5}\right\}\)
\(\left(x;y\right)\in\left\{\left(5;7\right);\left(3;-9\right);\left(6;3\right);\left(2;-5\right);\left(8;1\right);\left(0;-3\right);\left(12;0\right);\left(-4;-2\right);\left(20;-\dfrac{1}{2}\right);\left(-12;-\dfrac{7}{5}\right)\right\}\)
Mà \(x,y\inℕ\) nên các giá trị cần tìm là \(\left(x;y\right)\in\left\{\left(5;7\right);\left(6;3\right);\left(8;1\right);\left(12;0\right)\right\}\)
2)
(2x + 3)(y - 2) = 15
\(\left(2x+3\right)\inƯ\left(15\right)\)
\(\left(2x+3\right)\in\left\{1;-1;3;-3;5;-5;15;-15\right\}\)
Ta lập bảng
2x + 3 | 1 | -1 | 3 | -3 | 5 | -5 | 15 | -15 |
y - 2 | 15 | -15 | 5 | -5 | 3 | -3 | 1 | -1 |
(x; y) | (-1; 17) | (-2; -13) | (0; 7) | (-3; -3) | (1; 5) | (-4; -1) | (6; 3) | (-9; 1) |
Mà \(x,y\inℕ\) nên các giá trị cần tìm là \(\left(x;y\right)\in\left\{\left(0;7\right);\left(1;5\right);\left(6;3\right)\right\}\)
Ta có: xy+12=x-y
=> xy-x+y=-12
=>xy-x+y-1=-12-1
=>x(y-1)+(y-1)=-13
=>(x-1)(y-1)=-13=(-1).(13)=13.(-1)=(-13).1=1.(-13)
Ta có bảng sau:
Vậy (x;y) \(\in\){(2;-12);(0;14);(14;0);(-12;2)}
Ta có:
xy +12=x - y
<=> xy + 12 -x +y=0
<=>y[x +1] -[x+1] +13=0
<=> [x-1] . [x+1]=-13
=> x= 2,0,14,-12
y=-14,12,-2,0