l i m x → - ∞ x 2 + 2 x + 3 x 4 x 2 + 1 - x + 7 bằng:
A. 2/3
B. 1/2
C. (-2)/3
D. -1/2
K
Khách
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DH
4 tháng 7 2017
a, \(-\left(x+3\right)\left(x-4\right)+\left(x+1\right)\left(x-1\right)=10\)
\(\Rightarrow-\left(x^2-4x+3x-12\right)+x^2-1=10\)
\(\Rightarrow-x^2+x+12+x^2-1=10\)
\(\Rightarrow x=10+1-12\Rightarrow x=-1\)
b, \(\left(2x-1\right)\left(x-2\right)-\left(x+3\right)\left(2x-7\right)=3\)
\(\Rightarrow2x^2-4x-x+2-\left(2x^2-7x+6x-21\right)=3\)
\(\Rightarrow2x^2-5x+2-2x^2+x+21=3\)
\(\Rightarrow-4x=3-21-2\Rightarrow-4x=-20\)
\(\Rightarrow x=5\)
Các câu còn lại làm tương tự! Phá ngoặc ra!
Chúc bạn học tốt!!!
20 tháng 6 2015
Tính nhanh mỗi biểu thức sau:
a, 0 + 1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10 + 11 + 12 + 13 + 14 + 15 + 16 + 17 + 18 + 19 + 20
= (0 + 20) + (1 + 19) + (2 + 18) + (3 + 17) + (4 + 16) + (5 + 15) + (6 + 14) + (7 + 13) + (8 + 12) + (9 + 11) + 10
= 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 20 + 10
= 20 x 10 + 10
= 200 + 10
= 210
b, 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x (4 x 9 - 36)
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x (36 - 36)
= 1 x 2 x 3 x 4 x 5 x 6 x 7 x 8 x 9 x 0
= A x 0
= 0
c, (81 - 7 x 9 - 18) : (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= (81 - 63 - 18) : (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= (18 - 18) : (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= 0 :(1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9)
= 0 : A
= 0
d, (6 x 5 + 7 - 37) x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= (30 + 7 - 37) x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= (37 - 37) x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= 0 x (1 + 2 + 3 + 4 + 5 + 6 + 7 + 8 + 9 + 10)
= 0 x A
= 0
e, (11 x 9 - 100 + 1) : (1 x 2 x 3 x 4 x ... x 10)
= (99 - 100 + 1) : (1 x 2 x 3 x 4 x ... x 10)
= (99 + 1 - 100) : (1 x 2 x 3 x 4 x ... x 10)
= (100 - 100) : (1 x 2 x 3 x 4 x ... x 10)
= 0 : (1 x 2 x 3 x 4 x ... x 10)
= 0 : A
= 0
g, (m : 1 - m x 1) : (m x 2008 + m x 2008)
= (m - m) : (m x 2008 + m x 2008)
= 0 : (m x 2008 + m x 2008)
= 0 : A
= 0
h, (2 + 4 + 6 + 8 + m x n) x (324 x 3 - 972)
= (2 + 4 + 6 + 8 + m x n) x (972 - 972)
= (2 + 4 + 6 + 8 + m x n) x 0
= A x 0
= 0
l, (1 + 2 + 3 + ... + 99) x (13 x 15 - 12 x 15 - 15)
= (1 + 2 + 3 + ... + 99) x (15 x (13 - 12 - 1))
= (1 + 2 + 3 + ... + 99) x (15 x 0)
= (1 + 2 + 3 + ... + 99) x 0
= A x 0
= 0
i, (0 x 1 x 2 x...x 99 x 100) : (2 + 4 + 6 +...+ 98)
= 0 x : (2 + 4 + 6 +...+ 98)
= 0 x A
= 0
k, (0 + 1 + 2 +...+ 97 + 99) x (45 x 3 - 45 x 2 - 45)
= (0 + 1 + 2 +...+ 97 + 99) x (45 x (3 - 2 - 4))
= (0 + 1 + 2 +...+ 97 + 99) x (45 x 0)
= (0 + 1 + 2 +...+ 97 + 99) x 0
= A x 0
= 0
PN
12 tháng 9 2017
a) \(\dfrac{x}{x+1}=\dfrac{x+5}{x+7}\)
\(\Leftrightarrow x\left(x+7\right)=\left(x+1\right)\left(x+5\right)\)
\(\Leftrightarrow x^2+7x=\left(x+1\right)x+\left(x+1\right).5\)
\(\Leftrightarrow x^2+7x=x^2+x+5x+5\)
\(\Leftrightarrow x^2+7x=x^2+6x+5\)
\(\Leftrightarrow x^2+7x-6x-x^2=5\)
\(\Leftrightarrow x=5\)
Vậy...
b) \(\dfrac{x+7}{x+4}=\dfrac{x-1}{x-2}\)
\(\Leftrightarrow\left(x+7\right)\left(x-2\right)=\left(x+4\right)\left(x-1\right)\)
\(\Leftrightarrow\left(x+7\right)x-\left(x+7\right).2=\left(x+4\right)x-\left(x+4\right)\)
\(\Leftrightarrow x^2+7x-2x+14=x^2+4x-x-4\)
\(\Leftrightarrow x^2+5x+14=x^2+3x-4\)
\(\Leftrightarrow x^2+5x+14-3x-x^2=-4\)
\(\Leftrightarrow2x+14=-4\)
\(\Leftrightarrow2x=-18\)
\(\Leftrightarrow x=-9\)
Vậy...
c) \(\dfrac{x+2}{x-2}=\dfrac{x-3}{x+3}\)
\(\Leftrightarrow\left(x+2\right)\left(x+3\right)=\left(x-2\right)\left(x-3\right)\)
\(\Leftrightarrow\left(x+2\right)x+\left(x+2\right).3=\left(x-2\right)x-\left(x-2\right).3\)
\(\Leftrightarrow x^2+2x+3x+6=x^2-2x-3x+6\)
\(\Leftrightarrow x^2+5x+6=x^2-5x+6\)
\(\Leftrightarrow x^2+5x+6-6+5x-x^2=0\)
\(\Leftrightarrow10x=0\)
\(\Leftrightarrow x=0\)
Vậy...
HT
3 tháng 8 2021
4, Q = |x+\(\frac{1}{5}\) | -x +\(\frac{4}{7}\)
xét x \(\ge\) \(-\frac{1}{5}\)
Ta Có Q = |x+\(\frac{1}{5}\) | -x + \(\frac{4}{7}\) = x+\(\frac{1}{5}\) - x +\(\frac{4}{7}\) = \(\frac{27}{35}\) (1)
xét x \(< -\frac{1}{5}\)
Ta có Q = | x +\(\frac{1}{5}\) | - x + \(\frac{4}{7}\) = -x - \(\frac{1}{5}\) - x + \(\frac{4}{7}\) = -2x + \(\frac{13}{35}\)
với x \(< -\frac{1}{5}\)
=> -2x \(>\) \(\frac{2}{5}\)
=> -2x + \(\frac{13}{35}\) \(>\frac{27}{35}\) (2)
Từ (1) và (2) => MinQ = \(\frac{27}{35}\) khi \(x\ge-\frac{1}{5}\)
5 , D = |x| + |8-x|
D = |x| + |8-x| \(\ge\) |x+8-x| = |8| = 8
Dấu ''='' xảy ra khi x(8-x) \(\ge\) 0 <=> 0\(\le\)x\(\le\) 8
Vậy MinD = 8 khi \(0\le x\le8\)
6,L= |x - 2012| + |2011 - x|
L = |x-2012| + |2011-x| \(\ge\) | x-2012 + 2011 - x | = |-1| = 1
Dấu ''= '' xảy ra khi ( x-2012)(2011-x) \(\ge\) 0
HT
3 tháng 8 2021
làm nốt câu 6 nãy ấn nhầm
<=> 2011\(\le\) x \(\le\) 2012
Vậy MinL = 1 khi \(2011\le x\le2012\)
7 , E = | x- \(\frac{2006}{2007}\) | + |x-1|
Ta có :
E = |x-\(\frac{2006}{2007}\) | + |1-x|
E = | x - \(\frac{2006}{2007}\) | + |1-x| \(\ge\) | x - \(\frac{2006}{2007}\) + 1 - x | = \(\frac{1}{2007}\)
Dấu ''='' xảy ra khi (x- \(\frac{2006}{2007}\) ) ( 1-x ) \(\ge0\) <=> \(\frac{2006}{2007}\le x\le1\)
Vậy MinE = \(\frac{1}{2007}\) khi \(\frac{2006}{2007}\le x\le1\)
8 ,F = | x -\(\frac{1}{4}\) | + | \(x-\frac{3}{4}\) |
Ta có :
F = | x - \(\frac{1}{4}\) | + | \(\frac{3}{4}\) - x |
F = | x - \(\frac{1}{4}\) | + | \(\frac{3}{4}\) -x | \(\ge\) | x - \(\frac{1}{4}\) + \(\frac{3}{4}\) -x | = \(\frac{1}{2}\)
Dấu ''='' xảy ra khi ( x-\(\frac{1}{4}\) ) ( \(\frac{3}{4}-x\) ) \(\ge\) 0 <=> \(\frac{1}{4}\le x\le\frac{3}{4}\)
Vậy MinF = \(\frac{1}{2}\) khi \(\frac{1}{4}\le x\le\frac{3}{4}\)
QD
22 tháng 6 2017
d, \(\left(3x-2^4\right).7^3=2.7^4\)
\(\Rightarrow3x-2^4=2.7^4:7^3\)
\(\Rightarrow3x-16=2.7\\ \Rightarrow3x=14+16\\ \Rightarrow3x=30\Rightarrow x=10\)
Vậy.....
e, \(x-\left[42+\left(-28\right)\right]=-8\)
\(\Rightarrow x-14=-8\\ \Rightarrow x=6\)
Vậy.....
g, \(x-7=-5\)
\(\Rightarrow x=-5+7\Rightarrow x=2\)
Vậy.....
h, \(15-5\left(x+4\right)=-12-3\)
\(\Rightarrow15-5x-20=-15\)
\(\Rightarrow-5x=-15-15+20\)
\(\Rightarrow-5x=-10\Rightarrow x=2\)
Vậy.....
Chúc bạn học tốt!!!
AT
22 tháng 6 2017
d/ \(\left(3x-2^4\right)\cdot7^3=2\cdot7^4\)
\(\Rightarrow3x-16=\dfrac{2\cdot7^4}{7^3}=14\)
\(\Rightarrow3x=14+16=30\)
\(\Rightarrow x=\dfrac{30}{3}=10\)
e/ Đễ ==> tự lm thì tốt hơn nhé
g/ Đễ ==> tự lm thì tốt hơn nhé
h/ \(15-5\left(x+4\right)=-12-3\)
\(\Rightarrow15-5x-20=-15\)
\(\Rightarrow-5x=-15+20-15=-10\)
\(\Rightarrow x=\dfrac{-10}{-5}=2\)
i/ \(\left(7-x\right)-\left(25+7\right)=-25\)
\(\Rightarrow7-x-25-7=-25\)
\(\Rightarrow-x=-25-7+7+25\)
\(\Rightarrow-x=0\Rightarrow x=0\)
k/ \(\left|x+2\right|=0\Rightarrow x+2=0\Rightarrow x=-2\)
l/ \(\left|x-3\right|=7-\left(-2\right)\)
\(\Rightarrow\left|x-3\right|=9\)
\(\Rightarrow\left[{}\begin{matrix}x-3=9\\x-3=-9\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=12\\x=-6\end{matrix}\right.\)
m/ \(\left|x-5\right|=\left|-7\right|\Rightarrow\left|x-5\right|=7\)
\(\Rightarrow\left[{}\begin{matrix}x-5=7\\x-5=-7\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=12\\x=-2\end{matrix}\right.\)
21 tháng 1 2020
Mik ko biết làm phần a nha 
b) Ta có: (x+3)⋮(x−4)(x+3)⋮(x−4)
⇒(x+3)−(x−4)⋮(x−4)⇒(x+3)−(x−4)⋮(x−4)
⇒(x+3−x+4)⋮(x−4)⇒(x+3−x+4)⋮(x−4)
⇒7⋮(x−4)⇒7⋮(x−4)
⇒(x−4)∈Ư(7)⇒(x−4)∈Ư(7)
⇒x−4∈{−1;1;7;−7}⇒x−4∈{−1;1;7;−7}
⇒x∈{3;5;11;−3}⇒x∈{3;5;11;−3}
Vậy: x∈{3;5;11;−3}x∈{3;5;11;−3}
c)
Ta có: x-5 là bội của 7-x
⇒(x−5)⋮(7−x)⇒(x−5)⋮(7−x)
⇒(x−5)+(7−x)⋮(7−x)⇒(x−5)+(7−x)⋮(7−x)
⇒(x−5+7−x)⋮(7−x)⇒(x−5+7−x)⋮(7−x)
⇒2⋮(7−x)⇒2⋮(7−x)
⇒(7−x)∈Ư(2)⇒(7−x)∈Ư(2)
⇒(7−x)∈{−1;1;2;−2}⇒(7−x)∈{−1;1;2;−2}
⇒x∈{8;6;5;9}⇒x∈{8;6;5;9}
Vậy: x∈{8;6;5;9}
VM
22 tháng 9 2019
Bài 3:
\(\left|1-2x\right|+x+2=0\)
⇒ \(\left|1-2x\right|+x=0-2\)
⇒ \(\left|1-2x\right|+x=-2\)
⇒ \(\left|1-2x\right|=-2-x\)
⇒ \(\left[{}\begin{matrix}1-2x=-2-x\\1-2x=2+x\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}1+2=-x+2x\\1-2=x+2x\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}3=1x\\-1=3x\end{matrix}\right.\)
⇒ \(\left[{}\begin{matrix}x=3:1\\x=\left(-1\right):3\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=3\\x=-\frac{1}{3}\end{matrix}\right.\)
Vậy \(x\in\left\{3;-\frac{1}{3}\right\}.\)
Bài 4:
\(\left|5x-3\right|=\left|7-x\right|\)
⇒ \(\left[{}\begin{matrix}5x-3=7-x\\5x-3=x-7\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}5x+x=7+3\\5x-x=\left(-7\right)+3\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}6x=10\\4x=-4\end{matrix}\right.\)
⇒ \(\left[{}\begin{matrix}x=10:6\\x=\left(-4\right):4\end{matrix}\right.\) ⇒ \(\left[{}\begin{matrix}x=\frac{5}{3}\\x=-1\end{matrix}\right.\)
Vậy \(x\in\left\{\frac{5}{3};-1\right\}.\)
Chúc bạn học tốt!
16 tháng 6 2022
a: \(\Leftrightarrow2x-2+4x+8=-12\)
=>6x+6=-12
=>6x=-18
hay x=-3
b: \(\Leftrightarrow-10x-15-12+9x=13\)
=>-x-27=13
=>-x=40
hay x=-40
c: \(\Leftrightarrow-10x+70+20-5x=-15\)
\(\Leftrightarrow-15x=-105\)
hay x=7
d: \(\Leftrightarrow8x-12-7x+14=10\)
=>x+2=10
hay x=8
e: \(\Leftrightarrow-12x-18+14x+2=2\)
=>2x-16=2
hay x=9
TN
26 tháng 6 2017
\(a,\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\) \(=x^3+1-x^3+1=2\)
\(b,x\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)
\(=x\left(x^2-16\right)-\left(x^4-1\right)=x^3-16x-x^4+1\) \(c,\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2\)
\(=x^2-9-x^2-2x-1=-2x-10\)
\(d,\left(4x-3\right)\left(4x+3\right)-16x^2\)
\(=16x^2-9-16x^2=-9\)
\(e,\left(x+4\right)\left(x^2-4x+16\right)-x^3=x^3+64-x^3=64\)
25 tháng 8 2021
a) X=3/18
b)X=13/10
c)X=11/15
d)X=8/35
e)X=37/21
f)X=65/36
g)X=1/4
h)X=5/4
i)X=7/5
k)X=5/14
l)X=167/96
có nhiều bài khó nếu em ko bik thì kb với cj để cj giúp nha.
25 tháng 8 2021
a)3/8
b) 13/10
c) 11/15
d) 8/35
e) 37/21
f) 65/36
g) 1/4
h) 5/4
i) 7/5
k) 5/14
l) 167/96
-HT- :)))))))
Chọn C