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cho x1,..x2016 thỏa mãn:1/x1^2+...+1/x2016^2=1CM trong các số từ x1->x2016 có ít nhất 2 số bằng nhau
2016 vi khi cuoi ta nhan 2016 do nen co the la 2015 ban a ! violym thi kho lam 2045 nha
a) 2016x = 2017x
=> 2016x - 2017x =0
=> x(2016 - 2017) =0
=> x(-1)=0
=>x=0:(-1)=0
b) (x-5)2015=(x-5)2014
=> (x-5)2015 - (x-5)2014=0
=> (x-5)(2015-2014)=0
=> x-5=0
=>x=5
c)5x + 5x +2 =650
=> 10x + 2 =650
=> 10x =648
=> x = \(\frac{648}{10}=64,8\)
d) 2017x =2x
=> 2017x -2x =0
=> 2015x=0
=>x=0
1.
a.
\(\frac{1}{1\times2}+\frac{1}{2\times3}+\frac{1}{3\times4}+\frac{1}{4\times5}+\frac{1}{5\times6}=1-\frac{1}{2}+\frac{1}{2}-\frac{1}{3}+\frac{1}{3}-\frac{1}{4}+\frac{1}{4}-\frac{1}{5}+\frac{1}{5}-\frac{1}{6}=1-\frac{1}{6}=\frac{5}{6}\)
b.
Tích có 100 thừa số
=> n = 100
\(\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times\left(100-100\right)\)
\(=\left(100-1\right)\times\left(100-2\right)\times\left(100-3\right)\times...\times\left(100-99\right)\times0\)
\(=0\)
2.
a.
\(135\times789789-789\times135135=1001\times\left(135\times789-789\times135\right)=1001\times0=0\)
b.
\(\left(28\times9696-96\times2828\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=\left[101\times\left(28\times96-96\times28\right)\right]\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=\left(101\times0\right)\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=0\div\left(1\times2\times3\times...\times2015\times2016\right)\)
\(=0\)
3.
a.
\(\left[\left(x+32\right)-17\right]\times2=42\)
\(\left(x+32\right)-17=\frac{42}{2}\)
\(\left(x+32\right)-17=21\)
\(x+32=21+17\)
\(x+32=38\)
\(x=38-32\)
\(x=6\)
b.
\(125+\left(145-x\right)=175\)
\(145-x=175-125\)
\(145-x=50\)
\(x=145-50\)
\(x=95\)
a. Ta có: \(180=2^2.5.3^2\)
\(270=2.3^3.5\)
\(=>ƯCLN\left(180;270\right)=2.3^2.5=90\)
b.Ta có \(18=2.3^2;20=2^2.5;24=2^3.3\)
\(=>BCNN\left(18;20;24\right)=2^3.3^2.5=360\)
c.Ta có:\(48=2^4.3;66=2.3.11\)
\(=>ƯCLN\left(48;66\right)=2.3=6\)
\(=>ƯC\left(48;66\right)=Ư\left(6\right)=\left\{1;2;3;6\right\}\)
d.Ta có \(20=2^2.5;24=2^3.3;27=3^3\)
\(=>BCNN\left(20;24;27\right)=2^3.3^3.5=1080\)
\(=>BC\left(20;24;27\right)=B\left(1080\right)=\left\{0;1080;2160;...\right\}\)
\(#dhuyy\)
\(x^{2015}=x^{2016}\Leftrightarrow x^{2016}-x^{2015}=0\Leftrightarrow x^{2015}\left(x-1\right)=0\)
\(\orbr{\begin{cases}x^{2015}=0\\x-1=0\end{cases}\Leftrightarrow\orbr{\begin{cases}x=0\\x=1\end{cases}}}\)
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