2x-2-3*2x=-88
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a: =>2x-1/3=2
=>2x=7/3
=>x=7/6
b: Sửa đề: 1/11-5/22
\(\dfrac{8}{9}:\left(\dfrac{1}{11}-\dfrac{5}{22}\right)+\dfrac{5}{9}:\left(\dfrac{1}{15}-\dfrac{2}{3}\right)\)
\(=\dfrac{8}{9}:\dfrac{-3}{22}+\dfrac{5}{9}:\dfrac{-9}{15}\)
\(=\dfrac{8}{9}\cdot\dfrac{-22}{3}+\dfrac{5}{9}\cdot\dfrac{-5}{3}\)
\(=\dfrac{-66-25}{27}=\dfrac{-91}{27}\)
a, 2x - 15 = 17
2x = 17 +15
2x = 32
x =16
b, (7x - 11)3 =25 . 52 +88
(7x - 11)3 =888
7x =888+ 113 7x =2219 x= 317
\(2^{x-2}-3.2^x=-88\)
\(2^x:2^2-2^x:\frac{1}{3}=-88\)
\(2^x:\left(2^2-\frac{1}{3}\right)=-88\)
\(2^x:\frac{11}{3}=-88\)
\(2^x=-88.\frac{11}{3}\)
\(2^x=\frac{-968}{3}\)
\(2^{x-2}-\)\(3.2^x=-88\)
\(2^x:2^2-2^x.3=-88\)
\(2^x.\frac{1}{4}-\)\(2^x.3=-88\)
\(2^x.\left(\frac{1}{4}-3\right)=-88\)
\(2^x.\frac{-11}{4}=-88\)
\(2^x=-88:\frac{-11}{4}\)
\(2^x=32\)
\(2^x=2^5\)
\(\Rightarrow x=5\)
nhé
a)(2x-1)6=(2x-1)8
=> (2x-1)8-(2x-1)6=0
=> (2x-1)6.((2x-1)2-1)=0
+)th1(2x-1)6=0
+)th2((2x-1)2-1)=0
a) \(\left(2x-1\right)^6=\left(2x-1\right)^8\)
\(\Rightarrow\left(2x-1\right)\in\left\{\pm1;0\right\}\)
TH1 : \(2x-1=0\) TH2 : \(2x-1=-1\) TH3 : \(2x-1=1\)
\(2x=1\) \(2x=0\) \(2x=2\)
\(x=\frac{1}{2}\) \(x=0\) \(x=1\)
Vậy \(x\in\left\{\frac{1}{2};0;1\right\}\)
b) Tương tự
Áp dụng : \(\frac{1}{\sqrt{1}.2}< 2.\left(1-\frac{1}{\sqrt{2}}\right)\)
\(\frac{1}{\sqrt{2}.3}< 2.\left(\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}\right)\)
...................................
\(\frac{1}{\sqrt{2015}.2016}< 2.\left(\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}\right)\)
Cộng các BĐT trên với nhau được : \(\frac{1}{2}+\frac{1}{3\sqrt{2}}+\frac{1}{4\sqrt{3}}+...+\frac{1}{2016\sqrt{2015}}< 2\left(1-\frac{1}{\sqrt{2}}+\frac{1}{\sqrt{2}}-\frac{1}{\sqrt{3}}+...+\frac{1}{\sqrt{2015}}-\frac{1}{\sqrt{2016}}\right)=2\left(1-\frac{1}{\sqrt{2016}}\right)< 2\left(1-\frac{1}{\sqrt{2025}}\right)=\frac{88}{45}\)
Từ đó suy ra đpcm
Cái ............... là gì vậy bn
a/\(\left(x+3\right)\left(\frac{40}{x}+3\right)=88\)(đk: x\(\ne0\))
\(\Leftrightarrow40+\frac{120}{x}+3x+9=88\)
\(\Leftrightarrow3x+\frac{120}{x}=39\) \(\Leftrightarrow\frac{3x^2+120}{x}=39\)
\(\Leftrightarrow x^2+40-13x=0\Leftrightarrow\left(x-8\right)\left(x-5\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=8\\x=5\end{matrix}\right.\)(tm)
vậy x=8 hoặc x=5 là nghiệm của phương trình
b/ \(\frac{x-1}{2x+1}< \frac{1}{2}\left(x\ne-\frac{1}{2}\right)\)
\(\Leftrightarrow\frac{x-1}{2x+1}-\frac{1}{2}< 0\) \(\Leftrightarrow\frac{2x-2}{4x+2}-\frac{2x+1}{4x+2}< 0\)
\(\Leftrightarrow\frac{-3}{4x+2}< 0\) \(\Leftrightarrow4x+2>0\)(vì -3<0)
<=> x>-1/2(tm)
vậy x>-1/2 là nghiệm của phương trình
c/ \(\left\{{}\begin{matrix}x^3+1=2y\\y^3+1=2x\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x^3-y^3=2y-2x\left(1\right)\\x^3+1=2y\left(2\right)\end{matrix}\right.\)
(1)\(\Leftrightarrow\left(x-y\right)\left(x^2+xy+y^2\right)+2\left(x-y\right)=0\)
\(\Leftrightarrow\left(x-y\right)\left(x^2+xy+y^2+2\right)=0\)
\(\Leftrightarrow x=y\)(vì x^2 +xy+y^2 +2>0)
thay x=y vào (2) ta được:
\(x^3-2x+1=0\Leftrightarrow\left(x-1\right)\left(x^2+x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\\left(x+\frac{1}{2}\right)^2=\frac{5}{4}\end{matrix}\right.\) \(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=\frac{\sqrt{5}-1}{2}\\x=\frac{-1-\sqrt{5}}{2}\end{matrix}\right.\)
vậy...
a, A = 27x3 + 54x2 + 36x + 4
=> A = (3x)3 + 2 . 3 . 9x2 + 3 . 3x . 4 + 8 - 4
=> A = [(3x)3 + 2 . 3 . (3x)2 + 3 . 3x . 22 + 23] - 4
=> A = (3x + 2)3 - 4
Thay x = -2002 vào A ta có: A = (3x + 2)3 - 4
=> A = [3 x (-2002) + 2]3 - 4 = [6006 + 2]3 - 4 = 60083 - 4
b, B = 2x2 + 4x + xy + 2y
=> B = 2x(x + 2) + y(x + 2)
=> B = (x + 2)(2x + y)
Thay x = 88; y = -76 vào B
=> B = (88 + 2)[2 . 88 + (-76)]
=> B = 90 . [176 + (-76)] = 90 . 100 = 9000