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LN
26 tháng 10 2016
( 3x-5 /9 )^2002 > 0 ; ( 3y+0,4/3 )^2004 > 0
=> (3x-5/9 )^2002 = 0 và ( 3y + 0,4 / 3 )^2004 = 0
=> 3x - 5 = 0
3x = 5
x = 5/3
=> 3y + 0,4 = 0
3y = -0,4
y= -2/15
6 tháng 11 2023
\(\left(\dfrac{3x-5}{9}\right)^{2018}>=0\forall x\)
\(\left(\dfrac{3y+0,4}{3}\right)^{2020}>=0\forall y\)
Do đó: \(\left(\dfrac{3x-5}{9}\right)^{2018}+\left(\dfrac{3y+0,4}{3}\right)^{2020}>=0\forall x,y\)
Dấu '=' xảy ra khi \(\left\{{}\begin{matrix}\dfrac{3x-5}{9}=0\\\dfrac{3y+0,4}{3}=0\end{matrix}\right.\)
=>\(\left\{{}\begin{matrix}3x-5=0\\3y+0,4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{5}{3}\\y=-\dfrac{0.4}{3}=-\dfrac{2}{15}\end{matrix}\right.\)
TN
17 tháng 8 2015
bai 2: a) \(2^{30}=\left(2^3\right)^{10}=8^{10}\)
\(3^{20}=\left(3^2\right)^{10}=9^{10}\)
vi 810 <910 nen 230 <320
b) \(5^{202}=\left(5^2\right)^{101}=25^{101}\)
\(2^{505}=\left(2^5\right)^{101}=32^{101}\)
vi 25101 <32101 nen 5202 <2505
c) \(333^{444}=\left(3.111\right)^{444}=3^{444}.111^{444}=\left(3^4\right)^{111}.111^{444}=81^{111}.111^{444}\)
\(444^{333}=\left(4.111\right)^{333}=4^{333}.111^{333}=\left(4^3\right)^{111}.111^{333}=64^{111}.111^{333}\)
vi 81111>64111 va 111444>111333
nen 333444>444333
bai 3 : \(\left(\frac{1}{3}\right)^{2n-1}=3^5\)
\(\left(\frac{1}{3}\right)^{2n-1}=\left(\frac{1}{3}\right)^{-5}\)
2n-1=-5
2n=-5+1
2n=-4
n=-4:2
n=-2
Bai 4 : 3x-5/9=0 va 3y+0,4/3=0
3x=5/9 va 3y=2/15
x=5/27 va y=2/45
Bai 5:
A=75. {42002.(42+1)+....+(42+1)+1)+25
A=75.{42002.20+...+20+1}+25
A=75.{20.(42002+...+1)+1}+25
A=75.20.(42002+..+1)+75+25
A=1500.(42002+...+1)+100
A=100.{15.(42002+...+1)+1} chia het cho 100
1 tháng 11 2020
\(\left(\frac{3x-5}{9}\right)^{2018}+\left(\frac{3y+0,4}{3}\right)^{2020}=0\)
Ta có : \(\hept{\begin{cases}\left(\frac{3x-5}{9}\right)^{2018}\ge0\forall x\\\left(\frac{3y+0,4}{3}\right)^{2020}\ge0\forall y\end{cases}}\Rightarrow\left(\frac{3x-5}{9}\right)^{2018}+\left(\frac{3y+0,4}{3}\right)^{2020}\ge0\forall x,y\)
Dấu "=" xảy ra <=> \(\hept{\begin{cases}\frac{3x-5}{9}=0\\\frac{3y+0,4}{3}=0\end{cases}}\Leftrightarrow\hept{\begin{cases}3x-5=0\\3y+0,4=0\end{cases}}\Leftrightarrow\hept{\begin{cases}x=\frac{5}{3}\\y=-\frac{2}{15}\end{cases}}\)
PQ
1
13 tháng 7 2021
Ta có: \(\left(x-\dfrac{1}{5}\right)^{2004}\ge0\forall x\)
\(\left(y+\dfrac{2}{5}\right)^{100}\ge0\forall y\)
\(\left(z-3\right)^{678}\ge0\forall z\)
Do đó: \(\left(x-\dfrac{1}{5}\right)^{2004}+\left(y+\dfrac{2}{5}\right)^{100}+\left(z-3\right)^{678}\ge0\forall x,y,z\)
Dấu '=' xảy ra khi \(\left(x,y,z\right)=\left(\dfrac{1}{5};\dfrac{-2}{5};3\right)\)
LD
2
17 tháng 1 2022
Vì \(\left(x-\dfrac{1}{5}\right)^{2004}\ge0,\left(y+0,4\right)^{100}\ge0,\left(z-3\right)^{678}\ge0\)
\(\Rightarrow\left(x-\dfrac{1}{5}\right)^{2004}+\left(y+0,4\right)^{100}+\left(z-3\right)^{678}\ge0\)
Dấu "=" xảy ra \(\Leftrightarrow\left\{{}\begin{matrix}x-\dfrac{1}{5}=0\\y+0,4=0\\z-3=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{1}{5}\\y=-0,4\\z=3\end{matrix}\right.\)
Vậy \(\left(x,y,z\right)=\left(\dfrac{1}{5};-0,4;3\right)\)
17 tháng 1 2022
Vì \(\left(x-\dfrac{1}{5}\right)^{2004}\ge0\forall x\)
\(\left(y+0,4\right)^{100}\ge\forall y\)
\(\left(z-3\right)^{678}\ge0\forall z\)
\(\Rightarrow\left(x-\dfrac{1}{5}\right)^{2004}+\left(y+0,4\right)^{100}+\left(z-3\right)^{678}\ge0\)
mà \(\left(x-\dfrac{1}{5}\right)^{2004}+\left(y+0,4\right)^{100}+\left(z-3\right)^{678}=0\)
Dấu ''='' xảy ra khi \(x=\dfrac{1}{5};y=-0,4;z=3\)
AL
0
\(\left(3x-\frac{5}{9}\right)^{2002}+\left(3y+\frac{0,4}{3}\right)^{2004}=0\)
Ta thấy \(\left(3x-\frac{5}{9}\right)^{2002}\ge0\text{ với mọi x}\\ \left(3y+\frac{0,4}{3}\right)^{2004}\ge0\text{ với mọi y}\)
Mà \(\left(3x-\frac{5}{9}\right)^{2002}+\left(3y+\frac{0,4}{3}\right)^{2004}=0\)
\(\Rightarrow\left\{{}\begin{matrix}\left(3x-\frac{5}{9}\right)^{2002}=0\\\left(3y+\frac{0,4}{3}\right)^{2004}=0\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}3x-\frac{5}{9}=0\\3y+\frac{0,4}{3}=0\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}3x=\frac{5}{9}\\3y=\frac{-0,4}{3}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}x=\frac{\frac{5}{9}}{3}\\y=\frac{\frac{-0,4}{3}}{3}\end{matrix}\right.\\ \Rightarrow\left\{{}\begin{matrix}x=\frac{5}{27}\\y=\frac{-2}{45}\end{matrix}\right.\)
Vậy \(\left(x;y\right)=\left(\frac{5}{27};\frac{-2}{45}\right)\)
\(\left(3x-\frac{5}{9}\right)^{2002}+\left(3y+\frac{0,4}{4}\right)^{2004}=0\)
Ta có: \(\left\{{}\begin{matrix}\left(3x-\frac{5}{9}\right)^{2002}\ge0;\forall x,y\\\left(3y+\frac{0,4}{3}\right)^{2004}\ge0;\forall x,y\end{matrix}\right.\)\(\Rightarrow\left(3x-\frac{5}{9}\right)^{2002}+\left(3y+\frac{0,4}{4}\right)^{2004}\ge0;\forall x,y\)
Do đó \(\left(3x-\frac{5}{9}\right)^{2002}+\left(3y+\frac{0,4}{4}\right)^{2004}=0\)
\(\Leftrightarrow\left\{{}\begin{matrix}\left(3x-\frac{5}{9}\right)^{2002}=0\\\left(3y+\frac{0,4}{3}\right)^{2004}=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}3x-\frac{5}{9}=0\\3y+\frac{0,4}{3}=0\end{matrix}\right.\)
\(\Leftrightarrow\left\{{}\begin{matrix}x=\frac{5}{27}\\y=\frac{-2}{45}\end{matrix}\right.\)
Vậy ...