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a/ \(A=\frac{2x^3-6x^2+x-8}{x-3}=2x^2+1-\frac{5}{x-3}\)
Từ đây ta thấy A nguyên khi x - 3 là ước nguyên của 5 hay
\(\left(x-3\right)=\left(-5,-1,1,5\right)\)
\(\Rightarrow x=\left(-2,2,4,8\right)\)
b/ \(B=\frac{x^4-16}{x^4-4x^3+8x^2-16x+16}=\frac{\left(x^2+4\right)\left(x-2\right)\left(x+2\right)}{\left(x^2+4\right)\left(x-2\right)^2}\)
\(=\frac{x+2}{x-2}=1+\frac{4}{x-2}\)
Để B nguyên thì x - 2 phải là ước nguyên của 4 hay
\(\left(x-2\right)=\left(-4,-2,-1,1,2,4\right)\)
\(\Rightarrow x=\left(-2,0,1,3,4,6\right)\)
vào thống kê xem link nhé:
Câu hỏi của Kim Trân Ni - Toán lớp 8 - Học toán với OnlineMath
\(A=\dfrac{3x^2-9x+x-3+2}{x-3}\)
\(B=\dfrac{x^2\left(x+2\right)+5\left(x+2\right)}{\left(x+2\right)^2}=\dfrac{x^2+5}{x+2}=x-2+\dfrac{9}{x+2}\)
Để A và B cùng là số nguyên thì
\(\left\{{}\begin{matrix}x-3\in\left\{1;-1;2;-2\right\}\\x+2\in\left\{1;-1;3;-3;9;-9\right\}\end{matrix}\right.\Leftrightarrow}\left\{{}\begin{matrix}x\in\left\{4;2;5;1\right\}\\x\in\left\{-1;-3;1;-5;7;-11\right\}\end{matrix}\right.\)
hay x=1
BÀI 1:
a) \(ĐKXĐ:\) \(\hept{\begin{cases}x-2\ne0\\x+2\ne0\end{cases}}\) \(\Leftrightarrow\)\(\hept{\begin{cases}x\ne2\\x\ne-2\end{cases}}\)
b) \(A=\left(\frac{2}{x-2}-\frac{2}{x+2}\right).\frac{x^2+4x+4}{8}\)
\(=\left(\frac{2\left(x+2\right)}{\left(x-2\right)\left(x+2\right)}-\frac{2\left(x-2\right)}{\left(x-2\right)\left(x+2\right)}\right).\frac{\left(x+2\right)^2}{8}\)
\(=\frac{2x+4-2x+4}{\left(x-2\right)\left(x+2\right)}.\frac{\left(x+2\right)^2}{8}\)
\(=\frac{x+2}{x-2}\)
c) \(A=0\) \(\Rightarrow\)\(\frac{x+2}{x-2}=0\)
\(\Leftrightarrow\) \(x+2=0\)
\(\Leftrightarrow\)\(x=-2\) (loại vì ko thỏa mãn ĐKXĐ)
Vậy ko tìm đc x để A = 0
p/s: bn đăng từng bài ra đc ko, mk lm cho
Bằng 00000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000000$