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11 tháng 12 2018
Ta có:\(31^{13}< 32^{13}=\left(2^5\right)^{13}=2^{65}\)
\(65^{11}>64^{11}=\left(2^6\right)^{11}=2^{66}\)
Mà: \(2^{66}>2^{65}\Rightarrow65^{11}>2^{66}>2^{65}>31^{13}\)
Vậy: \(31^{13}< 65^{11}\)
TT
2
N
28 tháng 8 2017
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LX
28 tháng 8 2017
1 , \(\sqrt{7}\)-\(\sqrt{2}\)> 1
2 , \(^{\left(\sqrt{11}-x\right)^2}\)
BT
21 tháng 9 2016
Có: \(a^3+b^3=c^3\Leftrightarrow\left(\frac{a}{c}\right)^3+\left(\frac{b}{c}\right)^3=1.\)
Đặt : \(\frac{a}{c}=x;\frac{b}{c}=y\). Suy ra \(0< x< 1;0< y< 1\).
Vì vậy: \(x^{2010}< x^3;y^{2010}< y^3.\)
Từ đó: \(x^{2010}+y^{2010}< x^3+y^3< 1\).
Suy ra: \(\left(\frac{a}{c}\right)^{2010}+\left(\frac{b}{c}\right)^{2010}< 1\)hay: \(a^{2010}+b^{2010}< c^{2010}.\)
311<411; 411=(22)11=222
1714>1614; 1614=(24)14=256
Vì 222<256=> 411<1614
=>311<1714