\(\dfrac{2x}{32}=1\)
\(\dfrac{2x}{32}=1\)
\(\dfrac{2x}{32}=1\)
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ND
1
NA
Nguyễn An Ninh
VIP
5 tháng 5 2023
Nhớ tick cho mình nha
\(\dfrac{1}{3}\)x2 + \(\dfrac{1}{x^2}\) - 8x + 32 = \(\dfrac{1}{x^2}\) - 2x + 8 ĐK: x ≠ 0
⇔\(\dfrac{1}{3}\)x2 + \(\dfrac{1}{x^2}\) - \(\dfrac{1}{x^2}\) - 8x + 2x + 32 - 8 = 0
⇔\(\dfrac{1}{3}\)x2 - 6x +24 = 0
⇔\(\left(x-12\right)\) \(\left(x-6\right)\) = 0
⇔\(\left[{}\begin{matrix}x-12=0\\x-6=0\end{matrix}\right.\)
⇔\(\left[{}\begin{matrix}x=12\left(tm\right)\\x=6\left(tm\right)\end{matrix}\right.\)
⇒ S = \(\left\{12;6\right\}\)
11 tháng 10 2021
a) \(\dfrac{2x+3}{24}=\dfrac{3x-1}{32}\)
\(\Rightarrow32\left(2x+3\right)=24\left(3x-1\right)\)
\(\Rightarrow64x+96=72x-24\)
\(\Rightarrow8x=120\Rightarrow x=15\)
b) \(\dfrac{13x-2}{2x+5}=\dfrac{76}{17}\)
\(\Rightarrow17\left(13x-2\right)=76\left(2x+5\right)\)
\(\Rightarrow221x-34=152x+380\)
\(\Rightarrow69x=414\Rightarrow x=6\)
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
28 tháng 10 2023
a, \(x^2\) - 19 = 5.9
\(x^2\) - 19 = 45
\(x^2\) = 45 + 19
\(x^2\) = 64
\(x^2\) = 82
\(x\) = 8
NT
Nguyễn Thị Thương Hoài
Giáo viên
VIP
28 tháng 10 2023
b, (2\(x\) + 1)3 = -0,001
(2\(x\) + 1)3 = (-0,1)3
2\(x\) + 1 = -0,1
2\(x\) = -0,1 - 1
2\(x\) = - 1,1
\(x\) = -1,1: 2
\(x\) = - 0,55
AH
Akai Haruma
Giáo viên
20 tháng 7 2020
2.
\(\text{VP}=\frac{1}{32}(2+\cos 2x-2\cos 4x-\cos 6x)\)
\(=\frac{1}{32}[2+\cos 2x-2(2\cos ^22x-1)-(4\cos ^32x-3\cos 2x)]\)
\(=\frac{1}{8}(-\cos ^32x-\cos ^22x+\cos 2x+1)=\frac{1}{8}(\cos 2x+1)(1-\cos ^22x)=\frac{1}{8}(\cos 2x+1)\sin ^22x\) (1)
\(\text{VT}=\sin ^2x\cos ^4x=\frac{1}{8}.(2\sin x\cos x)^2.2\cos ^2x=\frac{1}{8}\sin ^22x.(\cos 2x+1)(2)\)
Từ $(1);(2)$ ta có đpcm.
AH
Akai Haruma
Giáo viên
20 tháng 7 2020
1.
\(\sin ^8x-\cos ^8x=(\sin ^4x+\cos ^4x)(\sin ^4x-\cos ^4x)\)
\(=[(\sin ^2x+\cos ^2x)^2-2\sin ^2x\cos ^2x](\sin ^2x+\cos ^2x)(\sin ^2x-\cos ^2x)\)
\(=(1-2\sin ^2x\cos ^2x)(\sin ^2x-\cos ^2x)\)
\(=(1-\frac{\sin ^22x}{2})(-\cos 2x)=-\frac{(2-\sin ^22x)\cos 2x}{2}=-\frac{(1+\cos ^22x)\cos 2x}{2}\) (1)
\(-(\frac{7}{8}\cos 2x+\frac{1}{8}\cos 6x)=\frac{-7}{8}\cos 2x-\frac{1}{8}(4\cos ^32x-3\cos 2x)=-\frac{\cos 2x+\cos ^32x}{2}\)
\(=\frac{-\cos 2x(\cos ^22x+1)}{2}\) (2)
Từ $(1);(2)$ ta có đpcm.
PN
9 tháng 5 2021
a, Với \(x=3\)\(=>A=\frac{x-1}{2}=\frac{3-1}{2}=\frac{2}{2}=1\)
Vậy A = 1 khi x = 3
b, Ta có : \(B=\frac{1}{x}-\frac{x}{2x+1}+\frac{2x^2-3x-1}{x\left(2x+1\right)}\)
\(=\frac{2x+1}{x\left(2x+1\right)}-\frac{x^2}{x\left(2x+1\right)}+\frac{2x^2-3x-1}{x\left(2x+1\right)}\)
\(=\frac{x^2-3x+2x+1-1}{x\left(2x+1\right)}=\frac{x^2-x}{x\left(2x+1\right)}=\frac{x\left(x-1\right)}{x\left(2x+1\right)}=\frac{x-1}{2x+1}\)
PN
9 tháng 5 2021
Ta có : \(A=\frac{x-1}{2};B=\frac{x-1}{2x+1}\)
\(=>C=A:B=\frac{x-1}{2}:\frac{x-1}{2x+1}=\frac{2x+1}{2}=x+\frac{1}{2}\)
đề sai bạn ơi
7 tháng 10 2021
9) \(\left\{{}\begin{matrix}\dfrac{7}{2x+y}+\dfrac{4}{2x-y}=74\\\dfrac{3}{2x+y}+\dfrac{2}{2x-y}=32\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{21}{2x+y}+\dfrac{12}{2x-y}=222\\\dfrac{21}{2x+y}+\dfrac{14}{2x-y}=224\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{2}{2x-y}=2\\\dfrac{7}{2x+y}+\dfrac{4}{2x-y}=74\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}2x+y=\dfrac{1}{10}\\2x-y=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}-2y=\dfrac{9}{10}\\2x+y=\dfrac{1}{10}\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}y=-\dfrac{9}{20}\\x=\dfrac{11}{40}\end{matrix}\right.\)
10) \(\left\{{}\begin{matrix}x=2y-1\\2x-y=5\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}2x-4y=-2\\2x-y=5\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=2y-1\\3y=7\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{11}{3}\\y=\dfrac{7}{3}\end{matrix}\right.\)
11) \(\left\{{}\begin{matrix}3x-6=0\\2y-x=4\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}3x=6\\y=\dfrac{x+4}{2}\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=3\end{matrix}\right.\)
12) \(\left\{{}\begin{matrix}2x+y=5\\x+7y=9\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}2x+y=5\\2x+14y=18\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}2x+y=5\\13y=13\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=2\\y=1\end{matrix}\right.\)
7 tháng 10 2021
13) \(\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{4}{y}=2\\\dfrac{4}{x}-\dfrac{5}{y}=3\end{matrix}\right.\)(ĐKXĐ: \(x,y\ne0\))
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{12}{x}-\dfrac{16}{y}=8\\\dfrac{12}{x}-\dfrac{15}{y}=9\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{3}{x}-\dfrac{4}{y}=2\\\dfrac{1}{y}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{2}\left(tm\right)\\y=1\left(tm\right)\end{matrix}\right.\)
14) \(\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{12}\\\dfrac{8}{x}+\dfrac{15}{y}=1\end{matrix}\right.\)(ĐKXĐ: \(x,y\ne0\))
\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{8}{x}+\dfrac{8}{y}=\dfrac{2}{3}\\\dfrac{8}{x}+\dfrac{15}{y}=1\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{1}{x}+\dfrac{1}{y}=\dfrac{1}{12}\\\dfrac{7}{y}=\dfrac{1}{3}\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}x=28\left(tm\right)\\y=21\left(tm\right)\end{matrix}\right.\)
15) \(\left\{{}\begin{matrix}2\sqrt{x-1}-\sqrt{y-1}=1\\\sqrt{x-1}+\sqrt{y-1}=2\end{matrix}\right.\)(ĐKXĐ: \(x\ge1,y\ge1\))
\(\Leftrightarrow\left\{{}\begin{matrix}3\sqrt{x-1}=3\\\sqrt{x-1}+\sqrt{y-1}=2\end{matrix}\right.\)\(\Leftrightarrow\left\{{}\begin{matrix}\sqrt{x-1}=1\\\sqrt{y-1}=1\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x-1=1\\y-1=1\end{matrix}\right.\)\(\Leftrightarrow x=y=2\left(tm\right)\)
20 tháng 11 2021
\(a,=\dfrac{1}{2}\left[\left(x^2+y^2\right)^2-4x^2y^2\right]\\ =\dfrac{1}{2}\left(x^2-2xy+y^2\right)\left(x^2+2xy+y^2\right)\\ =\dfrac{1}{2}\left(x-y\right)^2\left(x+y\right)^2\\ b,=\left(3x-\dfrac{1}{2}y\right)\left(9x^2+\dfrac{3}{2}xy+\dfrac{1}{4}y^2\right)\\ c,=\dfrac{1}{2}\left(x^2+\dfrac{1}{2}x+\dfrac{1}{16}\right)=\dfrac{1}{2}\left(x+\dfrac{1}{4}\right)^2\)
22 tháng 6 2022
c: \(\Leftrightarrow2x+2x-6=12-2x\)
=>4x-6=12-2x
=>6x=18
hay x=3
b: \(\Leftrightarrow\left(x-1\right)\left(x+1\right)+x=2x-1\)
\(\Leftrightarrow x^2-1+x=2x-1\)
=>x2-x=0
=>x(x-1)=0
=>x=0(loại) hoặc x=1(nhận)
28 tháng 2 2018
lớp 9 gì như lớp 6 thế
a) đề sai
c) <=>x/3 +x/3 -1 =2-x/3
<=>3.x/3 =3 => x=3
b) x<> 0; -2 <=>
x^2 -1 +x =2x-1
<=>x^2 -x =0 => x =0 (l) x =1 nhận
d ; <=> (x+1)/65+1 +(x+3)/63 +1 =(x+5)/61+1 +(x+7)/59+1
<=>(x+66) [1/65+1/63-1/61-1/59] =0
[...] khác 0
x=-66
cả 3 bài đều giống nhau nên mình làm 1 bài thôi nhé
\(\dfrac{2x}{32}=1\Rightarrow2x=32\)
x = 32 : 2
x = 16
\(\dfrac{2x}{32}=1\)
\(\Rightarrow2x.1=32.1\)
\(\Rightarrow2x=32\)
\(\Rightarrow x=16\)