Tìm \(x\in Z\)
để A=\(\frac{1-2x}{x+3}\in Z\)
K
Khách
Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
Những câu hỏi liên quan
10 tháng 6 2018
a) ta có: \(A=\frac{2x}{x-2}=\frac{2x-4+4}{x-2}=\frac{2.\left(x-2\right)+4}{x-2}=\frac{2.\left(x-2\right)}{x-2}+\frac{4}{x-2}=2+\frac{4}{x-2}\)
Để \(A\inℤ\)
\(\Rightarrow\frac{4}{x-2}\inℤ\)
\(\Rightarrow4⋮x-2\Rightarrow x-2\inƯ_{\left(4\right)}=\left(4;-4;2;-2;1;-1\right)\)
nếu x -2 = 4 => x = 6 (TM)
x- 2= - 4 => x= - 2 (TM)
x- 2= 2 => x = 4 (TM)
x- 2 = -2 => x = 0 (TM)
x - 2 = 1 => x = 3 (TM)
x - 2 = -1 => x= 1 (TM)
KL: \(x\in\left(6;-2;4;0;3;1\right)\)
c) ta có: \(C=\frac{x^2+2}{x+1}=\frac{\left(x+1\right).\left(x-1\right)+3}{x+1}=\frac{\left(x+1\right).\left(x-1\right)}{x+1}+\frac{3}{x+1}\)\(=x-1+\frac{3}{x+1}\)
Để \(C\inℤ\)
\(\Rightarrow\frac{3}{x+1}\inℤ\)
\(\Rightarrow3⋮x+1\Rightarrow x+1\inƯ_{\left(3\right)}=\left(3;-3;1;-1\right)\)
nếu x + 1 = 3 => x = 2 (TM)
x + 1 = - 3 => x = -4 (TM)
x + 1 = 1 => x = 0
x + 1 = -1 => x = -2 (TM)
KL: \(x\in\left(2;-4;0;-2\right)\)
p/s
B
8 tháng 12 2016
a) \(A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{x^2-3x+2}\)
\(\Leftrightarrow A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{x^2-x-2x+2}\)
\(\Leftrightarrow A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{x\left(x-1\right)-2\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{4x-1}{x-2}-\frac{x-3}{x-1}+\frac{-2x+4}{\left(x-1\right)\left(x-2\right)}\)
\(\Leftrightarrow A=\frac{\left(4x-1\right)\left(x-1\right)-\left(x-3\right)\left(x-2\right)-2x+4}{\left(x-2\right)\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{4x^2-4x-x+1-x^2+2x+3x-6-2x+4}{\left(x-2\right)\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{3x^2-2x-1}{\left(x-2\right)\left(x-1\right)}\)
\(\Leftrightarrow A=\frac{3x^2-3x+\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}\)\(=\frac{3x\left(x-1\right)+\left(x-1\right)}{\left(x-2\right)\left(x-1\right)}\)\(=\frac{\left(x-1\right)\left(3x+1\right)}{\left(x-2\right)\left(x-1\right)}\)\(=\frac{3x+1}{x-2}\)
b)\(\frac{3x+1}{x-2}=\frac{3x-6+7}{x-2}=\frac{3x-6}{x-2}+\frac{7}{x-2}=3+\frac{7}{x-2}\)
Ta có : \(x-2\inƯ_7\left\{-7;-1;1;7\right\}\)
\(\Rightarrow\left[\begin{array}{nghiempt}x-2=-7\\x-2=-1\\x-2=1\\x-2=7\end{array}\right.\)\(\Rightarrow\left[\begin{array}{nghiempt}\text{x=-5}\\\text{x=1}\\\text{x=3}\\\text{x}=9\end{array}\right.\)
\(\text{x}=1\) (loại)
Vậy giá trị nguyên tập hợp x là:
x=-5;3;9
KN
18 tháng 8 2021
a. ĐKXĐ : \(x\ne\frac{1}{2};\frac{5}{2};4;-\frac{3}{2};\frac{1\pm\sqrt{43}}{2}\)
\(A=\left(\frac{2x-3}{4x^2-12x+5}+\frac{3x-8}{13x-2x^2-20}-\frac{3}{2x-1}\right):\frac{21+2x-2x^2}{4x^2+4x-3}+\)
\(=\left(\frac{2x-3}{\left(2x-1\right)\left(2x-5\right)}-\frac{3x-8}{\left(2x-5\right)\left(x-4\right)}-\frac{3}{2x-1}\right).\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{\left(2x-3\right)\left(x-4\right)-\left(3x-8\right)\left(2x-1\right)-3\left(2x-5\right)\left(x-4\right)}{\left(2x-1\right)\left(2x-5\right)\left(x-4\right)}.\frac{\left(2x-1\right)\left(2x+3\right)}{21+2x-2x^2}+1\)
\(=\frac{-10x^2+47x-56}{\left(2x-5\right)\left(x-4\right)}.\frac{2x+3}{-2x^2+2x+21}+1\) số to wa
NX
2
CH
Cô Hoàng Huyền
Admin
VIP
24 tháng 1 2018
Ta có: \(\frac{1-2x}{x+3}=\frac{-2\left(x+3\right)+7}{x+3}=-2+\frac{7}{x+3}\)
Để \(\frac{1-2x}{x+3}\in Z\Leftrightarrow x+3\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\)
Vậy nên \(x\in\left\{-10;-4;-2;4\right\}\)
DT
1
28 tháng 9 2016
Ta có:
\(B=\frac{2x^3+x^2+2x+4}{2x+1}=\frac{x^2.\left(2x+1\right)+2x+1+3}{2x+1}\)
\(B=\frac{\left(2x+1\right).\left(x^2+1\right)+3}{2x+1}\)
\(B=\frac{\left(2x+1\right).\left(x^2+1\right)}{2x+1}+\frac{3}{2x+1}\)
\(B=x^2+1+\frac{3}{2x+1}\)
Do x nguyên nên x2 + 1 nguyên
Để B nguyên thì \(\frac{3}{2x+1}\) nguyên
\(\Rightarrow3⋮2x+1\)
\(\Rightarrow2x+1\in\left\{1;-1;3;-3\right\}\)
\(\Rightarrow2x\in\left\{0;-2;2;-4\right\}\)
\(\Rightarrow x\in\left\{0;-1;1;-2\right\}\)
Vậy \(x\in\left\{0;-1;1;-2\right\}\)
TT
1
NT
25 tháng 10 2016
2x+3 chia hết cho 3x+1
=>3(2x+3) chia hết cho 3x+1
=> 6x+9 chia hết cho 3x+1
=>2(3x+1)+7 chia hết cho 3x+1
=>7 chia hết cho 3x+1
=> 3x+1 thuộc Ư(7)=(1;7;-1;-7)
=> x thuộc 0;2
Ta có:
\(A=\frac{1-2x}{x+3}=\frac{1-2x-6+6}{x+3}=\frac{1-\left(2x+6\right)+6}{x+3}=\frac{\left(1+6\right)-\left(2x+6\right)}{x+3}=\frac{7-\left(2x+2\times3\right)}{x+3}=\frac{7-2\times\left(x+3\right)}{x+3}=\frac{7}{x+3}-\frac{2\times\left(x+3\right)}{x+3}=\frac{7}{x+3}-2\)
Để \(A=\frac{1-2x}{x+3}\in Z\) \(\left(x\ne-3\right)\)
thì \(\frac{7}{x+3}\in Z\) \(\left(x\ne-3\right)\)
\(\Rightarrow x+3\inƯ\left(7\right)=\left\{-7;-1;1;7\right\}\)
Ta có bảng sau:
mà \(x\in Z\) và \(x\ne-3\)
\(\Rightarrow x\in\left\{-10;-4;-2;4\right\}\)
Vậy \(x\in\left\{-10;-4;-2;4\right\}\) thì thỏa mãn đề bài.