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a) x + y = 10 ⇒ y = 10 − x ⇒ 3 x = 2 ( 10 − x ) ⇒ x = 4 ⇒ y = 6
b) y − x = − 4 ⇒ y = x − 4 ⇒ x − 2 x − 4 + 3 = 8 12 ⇒ x − 2 x − 1 = 8 12 ⇒ 12 x − 24 = 8 x − 8 ⇒ x = 4 ⇒ y = 0
c) x + 2 y = 12 ⇒ x = 12 − 2 y ⇒ 12 − 2 y 2 = y 5 ⇒ 60 − 10 y = 2 y ⇒ y = 5 ⇒ x = 2
2)
Tổng của 2 số là 2009
=> Trong 2 số phải có 1 số chẵn và 1 số lẻ
Mà số nguyên tố chẵn duy nhất là 2
=> 1 số là 2. Số còn lại là:
2009 - 2 = 2007 không là số nguyên tố
=> Tổng của 2 số nguyên tố không thể bằng 2009.
1)
Với p = 2 => p + 2 = 2 + 2 = 4 là hợp số (loại)
Với p = 3 => p + 2 = 3 + 2 = 5 là SNT
=> p + 4 = 3 + 4 = 7 là SNT (thỏa mãn)
Với p > 3 => p có dạng 3k + 1 hoặc 3k + 2 (k ∈ N*)
Nếu p = 3k + 1 => p + 2 = 3k + 1 + 2 = 3k + 3 chia hết cho 3 và lớn hơn 3
=> p + 2 là hợp số (loại)
Nếu p = 3k + 2 => p + 4 = 3k + 2 + 4 = 3k + 6 chia hết cho 3 và lớn hơn 3
=> p + 4 là hợp số (loại)
Vậy p = 3
a.
xy + 3x - 2y - 6 = 5
=>x(y + 3) - 2(y + 3) = 5
=>(x - 2)(y + 3) = 5.
Vì x, y thuộc Z nên x - 2, y + 3 thuộc Z
=> x - 2, y + 3 thuộc ước nguyên của 5
Lập bảng :
| x - 2 | -5 | -1 | 1 | 5 |
| y + 3 | -1 | -5 | 5 | 1 |
| x | -3 | 1 | 3 | 7 |
| y | -4 | -8 | 2 | -2 |
Vậy ......
b. Làm tương tự câu a.
c. Ta có x + y = 3 và x - y = 15
Bài này là tổng hiệu của cấp 1, áp dụng cách làm đó thì ta được số lớn là x = (3 + 15) : 2 = 9
Số bé là y = 9 - 15 = -6
d. Ta có : |x| + |y| = 1
=>|x| = 1 - |y|
Vì |x|, |y| >= 0 và |x| = 1 - |y| nên 0 =< |x|, |y| =< 1
Vì x, y thuộc Z nên x = 0 thì y = 1 hoặc -1 và ngược lại y = 0 thì x = 1 hoặc -1
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\(a,3x=2y\)và \(x+y=10\)
Ta cs : \(3x=2y\Rightarrow\frac{x}{2}=\frac{y}{3}\)
ADTC dãy tỉ số bằng nhau ta cs
\(\frac{x}{2}=\frac{y}{3}=\frac{x+y}{2+3}=\frac{10}{5}=2\)
\(\Leftrightarrow\frac{x}{2}=2\Leftrightarrow x=4\)
\(\Leftrightarrow\frac{y}{3}=2\Leftrightarrow y=6\)
\(c,\frac{x}{2}=\frac{y}{5}\)và \(x+2y=12\)
ADTC dãy tỉ số bằng nhau ta cs
\(\frac{x}{2}=\frac{y}{5}=\frac{x+2y}{2+2.5}=\frac{12}{12}=1\)
\(\Leftrightarrow\frac{x}{2}=1\Leftrightarrow x=2\)
\(\Leftrightarrow\frac{y}{5}=1\Leftrightarrow y=5\)
bạn k lm phần b hộ mình ak
ko ADTC dãy tỉ số = nhau đâu :((
\(b,\frac{x-2}{y+3}=\frac{8}{2}\)và \(y-x=-4\)
\(\frac{x-2}{8}=\frac{y+3}{2}\Leftrightarrow\frac{x-2}{8}=\frac{4y+12}{8}\)
\(\Leftrightarrow x-2=4y+12\)
\(\Leftrightarrow x-4y=12+2=14\Leftrightarrow x-4y=14\)
\(\Leftrightarrow x=14+4y\Leftrightarrow x=\frac{14y}{y}+\frac{4y}{1}\Leftrightarrow\frac{14y}{y}+\frac{4y}{y}=\frac{18y}{y}=18\)
Vậy x = 18
Thay x = 18
\(\frac{18-2}{y+3}=\frac{8}{2}\Leftrightarrow\frac{16}{y+3}=4\Leftrightarrow y+3=4\Leftrightarrow y=1\)
Vậy y = 1
ADCT là cái j hả bạn
a) Ta có : \(3x=2y\)=> \(\frac{x}{2}=\frac{y}{3}\)
Đặt \(\frac{x}{2}=\frac{y}{3}=k\Rightarrow\orbr{\begin{cases}x=2k\\y=3k\end{cases}}\)
=> x + y = 2k + 3k
=> 5k = 10
=> k = 2
Do đó : x = 2.2 = 4,y = 3.2 = 6
\(\frac{x-2}{y+3}=\frac{8}{2}\)=> 2(x - 2) = 8(y+3)
=> 2x - 4 = 8y + 24
=> 2x - 4 - 8y = 24
=> 2(x - 4y) = 28
=> x - 4y = 14
=> x = 14 + 4y
Lại có y - x = -4 nên y = -4 + x (1)
Thế vào (1) ta có : x = 14 + 4(-4 + x)
=> x = 14 + (-16) + 4x
=> x = -2 + 4x
=> x + 2 = 4x
=> 2 = 3x
=> x = 2/3
Thay x = 2/3 vào (1) ta có : y = -4 + 2/3 = \(\frac{-12+2}{3}=\frac{-10}{3}\)
Bạn Brainchild làm sai rồi nhé
c) \(\frac{x}{2}=\frac{y}{5}\)=> \(\frac{x}{2}=\frac{2y}{10}\)
Đặt \(\frac{x}{2}=\frac{2y}{10}=k\Rightarrow\orbr{\begin{cases}x=2k\\2y=10k\end{cases}}\)
=> x + 2y = 2k + 10k
=> 12k = 12
=> k = 1
Do đó : x = 2.1 = 2, 2y = 10.1 => 2y = 10 => y = 5
Vậy x = 2,y=5
Bạn Mun Già ơi , bạn k giúp mình câu B à
Nguyễn Thị Hằng câu b ngay chỗ \(\frac{x-2}{y+3}=\frac{8}{2}\)... đó bạn à
Bạn ơi mình xin lỗi nhé , mình k để ý thấy . Mình cảm ơn bạn rất nhiều