mk làm tới đây gòi mà hông bít làm nữa,mong mn giúp ạ
\(x^2\left(2+5x^2\right)=\dfrac{-195}{16}\)
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1.A= 1.2.3+2.3.4+...+29.30.31+x=15
\(4A=1.2.3.4+2.3.4.\left(5-1\right)+...+29.30.31.\left(32-28\right)+4x=60\)
\(\Rightarrow4A=1.2.3.4+2.3.4.5-1.2.3.4+...+29.30.31.32-28.29.30.31+4x=60\)
Từ đó suy ra nha bạn
2.\(\frac{2}{2.3}+\frac{2}{3.4}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
\(=\frac{2}{2\left(2+1\right)}+\frac{2}{3.\left(3+1\right)}+...+\frac{2}{x\left(x+1\right)}=\frac{2007}{2009}\)
\(=2.\left(\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+...+\frac{1}{x}-\frac{1}{x+1}\right)=\frac{2007}{2009}\)
\(=2.\left(\frac{1}{2}-\frac{1}{x+1}\right)=\frac{2007}{2009}\\ =1-\frac{2}{\left(x+1\right)}=\frac{2007}{2009}\)
\(\Rightarrow\frac{2}{x+1}=\frac{2}{2009}\Rightarrow x+1=2009\Rightarrow x=2008\)
\(=\dfrac{-8}{27}\cdot81+\dfrac{9}{16}\cdot32\)
=-24+18
=-6
1.
1.2 +2.3 +...+97.98
=1/3.(1.2.3 +2.3.3 +3.4.3 +...+97.98.3)
=1/3.(1.2.3 - 0.1.2+ 2.3.4 -1.2.3 + 3.4.5 -2.3.4 + ... +97.98.99 -96.97.98)
=1/3 . 97.98.99
= 313698
=>1.2 +2.3 +...+97.98-x=16
=>313698-x=16
=> x=313682
4.
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x-x=-x\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x=-x+x\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]:x=0\)
\(\left[\left(\frac{36}{x}-x\right):x-x\right]=0\)
\(\left(\frac{36}{x}-x\right):x=x\Rightarrow\frac{36}{x}-x=x^2\)
\(\frac{36}{x}=x^2+x=x\left(x+1\right)\Rightarrow36=x^2\left(x+1\right)\)
Mà Ư(36)={1;2;3;4;6;9;12;18;36}; 9 là số chính phương duy nhất bé hơn 36=> x2 = 9 => x=3
2 câu kia thì đợi một lúc.
Ta có: \(x^2+5y^2+2xy-4x-8y+2015\)
\(=\left(x^2+2xy+y^2\right)-\left(4x+8y\right)+4+\left(4y^2-4y+1\right)+2010\)
\(=[\left(x+y\right)^2-4\left(x+2y\right)+4]+\left(4y^2-4y+1\right)+2010\)
\(=\left(x+y-2\right)^2+\left(2y-1\right)^2+2010\)
mà \(\left(x+y-2\right)^2,\left(2y-1\right)^2\ge0\)
nên \(x^2+5y^2+2xy-4x-8y+2015\ge2010\)
Vậy MIN= 2010 \(\Leftrightarrow x=\frac{3}{2},y=\frac{1}{2}.\)
Tờ 1
41 It's very important to use body language in communication
42 Despite her age, she still leads an active life
43 My mother said that you had to decorate the room carefully
44 People recycle old cans to make new ones
45 Tim is always forgetting his homework
46 T
47 F
48 T
49 T
50 F
Tờ 2
17 C => hard
18 do => make
19 D => has
20 to go => going
21 A => At
22 B => to
23 C => beautifully
24 D => five-star
25 is => was
V
26 would travel
27 be
28 to buy
29 has spoken
30 Has - just been finished
VI
31 for
32 as
33 about
34 with
35 than
VII
36 development
37 exploration
38 behavior
39 deforestation
40 specialness
A = 0,5 - | x - 3,5 |
Vì | x - 3,5 | >= 0
=> A = 0,5 - | x - 3,5 | < = 0,5
Dấu ( = ) xảy ra khi : | x - 3,5 | = 0
x - 3,5 = 0
x = 3,5
Vậy A đạt GTLN là 0,5 khi x = 3,5
B = - | 1,4 - x | - 2
Vì | 1,4 - x | > = 0
=> B = - | 1,4 - x | - 2 < = - 2
Dấu ( = ) xảy ra khi : | 1,4 - x | = 0
1,4 - x = 0
x = 1,4
Vậy B đạt GTLN là -2 khi x = 1,4
A vì cái trị tuyệt đối ý nó luôn lớn hơn hoặc bằng 0 ý nên A luôn bé hơn hoặc bằng 0,5 ý vậy GTLN của A là 0,5 ý
B vì âm trị tuyệt đối luôn bé hơn hoặc bằng 0 ý nên B luôn bé hơn hoặc bằng -2 ý vậy GTLN của A là -2 ý
16x4 - 64 = 16(x4 - 4) = 16[(x2)2 - 22] = 16(x2 - 2)(x2 + 2) = 16[x2 -\(\left(\sqrt{2}\right)^2\)](x2 + 2) = 16\(\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\left(x^2+2\right)\)
\(16x^4-64\)
\(=16\left(x^4-4\right)\)
\(=16\left(x^2-2\right)\left(x^2+2\right)\)
\(=16\left(x^2-\left(\sqrt{2}\right)^2\right)\left(x^2+2\right)\)
\(=16\left(x-\sqrt{2}\right)\left(x+\sqrt{2}\right)\left(x^2+2\right)\)
Bài này ra kết quả trên là lớp 9 . Còn lớp 8 là : \(16\left(x^2-2\right)\left(x^2+2\right)\)
a)\(\left|x+\dfrac{2}{3}\right|=\dfrac{5}{6}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{2}{3}=\dfrac{-5}{6}\\x+\dfrac{2}{3}=\dfrac{5}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=\dfrac{-3}{2}\\x=\dfrac{1}{6}\end{matrix}\right.\)
b) \(\left(x-\dfrac{1}{3}\right)^2=\dfrac{4}{9}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{2}{3}\\x-\dfrac{1}{3}=\dfrac{-2}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-1}{3}\end{matrix}\right.\)
a) Ta có: \(\left|x+\dfrac{2}{3}\right|=\dfrac{5}{6}\)
\(\Leftrightarrow\left[{}\begin{matrix}x+\dfrac{2}{3}=-\dfrac{5}{6}\\x+\dfrac{2}{3}=\dfrac{5}{6}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=-\dfrac{3}{2}\\x=\dfrac{1}{6}\end{matrix}\right.\)
b) Ta có: \(\left(x-\dfrac{1}{3}\right)^2=\dfrac{4}{9}\)
\(\Leftrightarrow\left[{}\begin{matrix}x-\dfrac{1}{3}=\dfrac{2}{3}\\x-\dfrac{1}{3}=-\dfrac{2}{3}\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\dfrac{-1}{3}\end{matrix}\right.\)
Ta có\(\left\{{}\begin{matrix}x^2\left(2+5x^2\right)\ge0\\-\dfrac{195}{16}< 0\end{matrix}\right.\)
pt vô nghiệm