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2/ Ta có : 4x - 3 \(⋮\) x - 2
<=> 4x - 8 + 5 \(⋮\) x - 2
<=> 4(x - 2) + 5 \(⋮\) x - 2
<=> 5 \(⋮\)x - 2
=> x - 2 thuộc Ư(5) = {-5;-1;1;5}
Ta có bảng :
| x - 2 | -5 | -1 | 1 | 5 |
| x | -3 | 1 | 3 | 7 |
Bài 1:
a) 1014049
b)1998^2 - (1998+2)(1998-2) = 1998^2 - (1998^2 - 4)
= 1998^2 - 1998^2 +4
= 4
Bài 2:
a) n thuộc -7;-6;-4;-3
b) n thuộc -7;-1;1;7
c) n thuộc -3;1;3;7
XIN LỖI VÌ MÌNH KHÔNG GHI CÁCH GIẢI
CHÚC BẠN HỌC TỐT
Bài 1:
a, \(\left(x-2\right)^2=9\)
\(\Rightarrow x-2\in\left\{-3;3\right\}\Rightarrow x\in\left\{-1;5\right\}\)
b, \(\left(3x-1\right)^3=-8\)
\(\Rightarrow3x-1=-2\Rightarrow3x=-1\)
\(\Rightarrow x=-\dfrac{1}{3}\)
c, \(\left(x+\dfrac{1}{2}\right)^2=\dfrac{1}{16}\)
\(\Rightarrow x+\dfrac{1}{2}\in\left\{-\dfrac{1}{4};\dfrac{1}{4}\right\}\)
\(\Rightarrow x\in\left\{-\dfrac{3}{4};-\dfrac{1}{4}\right\}\)
d, \(\left(\dfrac{2}{3}\right)^x=\dfrac{4}{9}\)
\(\Rightarrow\left(\dfrac{2}{3}\right)^x=\left(\dfrac{2}{3}\right)^2\)
Vì \(\dfrac{2}{3}\ne\pm1;\dfrac{2}{3}\ne0\) nên \(x=2\)
e, \(\left(\dfrac{1}{2}\right)^{x-1}=\dfrac{1}{16}\)
\(\Rightarrow\left(\dfrac{1}{2}\right)^{x-1}=\left(\dfrac{1}{2}\right)^4\)
Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(x-1=4\Rightarrow x=5\)
f, \(\left(\dfrac{1}{2}\right)^{2x-1}=8\) \(\Rightarrow\left(\dfrac{1}{2}\right)^{2x-1}=\left(\dfrac{1}{2}\right)^{-3}\) Vì \(\dfrac{1}{2}\ne\pm1;\dfrac{1}{2}\ne0\) nên \(2x-1=-3\) \(\Rightarrow2x=-2\Rightarrow x=-1\) Chúc bạn học tốt!!!
Câu 1: Lời giải:
a, Đặt \(A=\dfrac{3x+7}{x-1}\).
Ta có: \(A=\dfrac{3x+7}{x-1}=\dfrac{3x-3+10}{x-1}=\dfrac{3x-3}{x-1}+\dfrac{10}{x-1}=3+\dfrac{10}{x-1}\)
Để \(A\in Z\) thì \(\dfrac{10}{x-1}\in Z\Rightarrow10⋮x-1\Leftrightarrow x-1\in U\left(10\right)=\left\{\pm1;\pm2;\pm5;\pm10\right\}\)
Ta có bảng sau:
| \(x-1\) | \(1\) | \(-1\) | \(2\) | \(-2\) | \(5\) | \(-5\) | \(10\) | \(-10\) |
| \(x\) | \(2\) | \(0\) | \(3\) | \(-1\) | \(6\) | \(-4\) | \(11\) | \(-9\) |
Vậy, với \(x\in\left\{-9;-4;-1;0;2;3;6;11\right\}\)thì \(A=\dfrac{3x+7}{x-1}\in Z\).
Câu 3:
a, Ta có: \(-\left(x+1\right)^{2008}\le0\)
\(\Rightarrow P=2010-\left(x+1\right)^{2008}\le2010\)
Dấu " = " khi \(\left(x+1\right)^{2008}=0\Rightarrow x+1=0\Rightarrow x=-1\)
Vậy \(MAX_P=2010\) khi x = -1
b, Ta có: \(-\left|3-x\right|\le0\)
\(\Rightarrow Q=1010-\left|3-x\right|\le1010\)
Dấu " = " khi \(\left|3-x\right|=0\Rightarrow x=3\)
Vậy \(MAX_Q=1010\) khi x = 3
c, Vì \(\left(x-3\right)^2+1\ge0\) nên để C lớn nhất thì \(\left(x-3\right)^2+1\) nhỏ nhất
Ta có: \(\left(x-3\right)^2\ge0\Rightarrow\left(x-3\right)^2+1\ge1\)
\(\Rightarrow C=\dfrac{5}{\left(x-3\right)^2+1}\le\dfrac{5}{1}=5\)
Dấu " = " khi \(\left(x-3\right)^2=0\Rightarrow x=3\)
Vậy \(MAX_C=5\) khi x = 3
d, Do \(\left|x-2\right|+2\ge0\) nên để D lớn nhất thì \(\left|x-2\right|+2\) nhỏ nhất
Ta có: \(\left|x-2\right|\ge0\Rightarrow\left|x-2\right|+2\ge2\)
\(\Rightarrow D=\dfrac{4}{\left|x-2\right|+2}\le\dfrac{4}{2}=2\)
Dấu " = " khi \(\left|x-2\right|=0\Rightarrow x=2\)
Vậy \(MAX_D=2\) khi x = 2
a, \(\left(2,8x-32\right):\dfrac{2}{3}=-90\)
\(\Rightarrow2,8x-32=-60\)
\(\Rightarrow2,8x=-28\)
\(\Rightarrow x=-10\)
Vậy x = -10
b, \(\left(4,5-2x\right):1\dfrac{4}{7}=\dfrac{11}{14}\)
\(\Rightarrow\left(4,5-2x\right):\dfrac{11}{7}=\dfrac{11}{14}\)
\(\Rightarrow4,5-2x=\dfrac{121}{98}\)
\(\Rightarrow2x=\dfrac{160}{49}\)
\(\Rightarrow x=\dfrac{80}{49}\)
Vậy \(x=\dfrac{80}{49}\)
\(a,\left(2,8x-32\right):\dfrac{2}{3}=-90\)
\(2,8x-32=-90.\dfrac{2}{3}\)
\(2,8x-32=-60\)
\(2,8x=-60+32\)
\(2,8x=-28\)
\(x=-28:2,8\)
\(x=-10\)
Vậy \(x=-10\)
\(b,\left(4,5-2x\right):1\dfrac{4}{7}=\dfrac{11}{14}\)
\(\left(4,5-2x\right):\dfrac{11}{7}=\dfrac{11}{14}\)
\(4,5-2x=\dfrac{11}{14}.\dfrac{11}{7}\)
\(4,5-2x=\dfrac{121}{98}\)
\(2x=4,5-\dfrac{121}{98}\)
\(2x=\dfrac{160}{49}\)
\(x=\dfrac{160}{49}:2\)
\(x=\dfrac{80}{49}\)
Vậy \(x=\dfrac{80}{49}\)
Bài 1 :
Để phân số \(A=\dfrac{n+6}{n-1}\in Z\left(n\in N\right)\) thì :
\(n+6⋮n-1\)
Mà \(n-1⋮n-1\)
\(\Leftrightarrow7⋮n-1\)
Vì \(n\in N\Leftrightarrow n-1\in N;n-1\inƯ\left(5\right)\)
\(\Leftrightarrow\left\{{}\begin{matrix}n-1=1\Leftrightarrow n=2\\n-1=5\Leftrightarrow n=6\end{matrix}\right.\) \(\left(tm\right)\)
Vậy ...............
Bài 2 :
Ta có :
\(11n+7⋮n\)
Mà \(n⋮n\)
\(\Leftrightarrow\left\{{}\begin{matrix}11n+7⋮n\\11n⋮n\end{matrix}\right.\)
\(\Leftrightarrow7⋮n\)
Vì \(n\in N\Leftrightarrow n\inƯ\left(7\right)=\left\{1;7\right\}\)
Vậy ................
bài 3 :
a) \(\left(5+\dfrac{4}{7}\right):x=13\)
\(\dfrac{39}{7}:x=13\)
\(x=\dfrac{39}{7}:13\)
\(x=\dfrac{1}{7}\)
Vậy .................
b) \(\left(2,8x+32\right):\dfrac{2}{3}=90\)
\(2,8x+32=90.\dfrac{2}{3}\)
\(2,8x+32=60\)
\(2,8x=60-32\)
\(2,8x=28\)
\(x=28:2,8\)
\(x=10\)
Vậy .........