l i m x → + ∞ 2 x 4 + x 3 - 2 x 2 - 3 x - 2 x 4 bằng:
A. -2
B. -1
C. 1
D. 2
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\(a,\left(x+1\right)\left(x^2-x+1\right)-\left(x-1\right)\left(x^2+x+1\right)\) \(=x^3+1-x^3+1=2\)
\(b,x\left(x-4\right)\left(x+4\right)-\left(x^2+1\right)\left(x^2-1\right)\)
\(=x\left(x^2-16\right)-\left(x^4-1\right)=x^3-16x-x^4+1\) \(c,\left(x-3\right)\left(x+3\right)-\left(x+1\right)^2\)
\(=x^2-9-x^2-2x-1=-2x-10\)
\(d,\left(4x-3\right)\left(4x+3\right)-16x^2\)
\(=16x^2-9-16x^2=-9\)
\(e,\left(x+4\right)\left(x^2-4x+16\right)-x^3=x^3+64-x^3=64\)
Bài 1:
Từ P(x) = 3x2+8x-4 = -4
=> 3x2+8x = 0
x(3x+8) = 0
=> x = 0 3x+8 = 0
=> x = 0 3x = 8
=> x = 8/3
Bài 2 :
Ta có x = -1 là nghiệm của đa thức f(x) = 2x2-x+m
=> f(-1) = 2(-1)2-(-1)+m = 0
=> 2+1+m = 0
=> 3+m = 0
m = 0-3
m = -3
b) Giải:
Ta có: \(4x+3⋮x-2\)
\(\Rightarrow4x-8+11⋮x-2\)
\(\Rightarrow4\left(x-2\right)+11⋮x-2\)
\(\Rightarrow11⋮x-2\)
\(\Rightarrow x-2\in\left\{1;-1;11;-11\right\}\)
\(\left[\begin{matrix}x-2=1\\x-2=-1\\x-2=11\\x-2=-11\end{matrix}\right.\Rightarrow\left[\begin{matrix}x=3\\x=1\\x=13\\x=-9\end{matrix}\right.\)
Vậy \(x\in\left\{3;1;13;-9\right\}\)
b.Ta có:(4x+3)=4x-4.2+8+3
=4(x-2)+11
Để(4x+3)chia hết cho (x-2)
#11chia hết cho (x-2)(#là khi và chỉ khi nhế!)
#x-2€ Ư(11)={±1;±11}
#x€{3;1;13;-9}
Vậy x€{3;1;13;-9}
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!!!
bài2
a, x-15=-63-4
=>x-15=-67
=>x=-52
b, -x+3=11
=>x=-11+3
=>x=-8
c,\(|\)x+2\(|\)-4=7
=>\(|\)x+2\(|\)=11
=>\(\left\{{}\begin{matrix}x+2=11\\x+2=-11\end{matrix}\right.\)=>\(\left\{{}\begin{matrix}x=9\\x=13\end{matrix}\right.\)
bài3
ta có:\(\left|y\right|\)=8
=>\(\left[{}\begin{matrix}y=8\\y=-8\end{matrix}\right.\)
TH1 x=5,y=8
=>x-y=5-8=-3
y-x=8-5=3
TH2x=5 ,y=-8
x-y=5--8=13
y-x=-8-5=-13
Baif:
a) x-15=-63-4
x-15=-67
x=-67+15
x=-52
b)-x+3=11
-x=11-3
-x=8
=> x=8
c)\(\left|x+2\right|-4=7\)
\(\left|x+2\right|\)=7+4=11
=> x+2=11 hoặc x+2=-11
x=11-2=9 hoặc x=-11-2=-13
Bài 3:
TH1: Nếu x=5 và y=8
thì x-y=5-8=-3
y-x=8-5=3
TH
: Nếu x=5 và y=-8
thì x-y=5-(-8)=13
y-x=(-8)-5=-13
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!!!
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/ \(\left|x-5\right|=\left|-7\right|\Rightarrow\left|x-5\right|=7\)
\(\Rightarrow\left[{}\begin{matrix}x-5=7\\x-5=-7\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}x=12\\x=-2\end{matrix}\right.\)
a. x4 + x2y2 + y4 = (x4 + 2x2y2 + y4) - x2y2
= (x2 + y2)2 – (xy)2
= [(x2 + y2) + xy] [(x2 + y2) – xy]
= (x2 + xy + y2)(x2 –xy + y2)
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
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 \(\frac{1}{4}\le x\le\frac{3}{4}\)
Đáp án B