Question

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So sánh: \(M=\frac{-2020}{55555^{66666}}\) và \(N=\frac{2020}{-66666^{55555}.11111^{11111}}\) 

Giúp mình nhé!

Answer 1

[Trần Công Mạnh]

Bg

Ta có: \(M=\frac{-2020}{55555^{66666}}\)và \(N=\frac{2020}{-66666^{55555}.11111^{11111}}\)

Xét \(M=\frac{-2020}{55555^{66666}}\):

=> \(M=\frac{-2020}{\left(11111.5\right)^{11111.6}}\)

=> \(M=\frac{-2020}{11111^{11111.6}.5^{11111.6}}\)

=> \(M=\frac{-2020}{11111^{11111.6}.5^{6^{11111}}}\)

=> \(M=\frac{-2020}{11111^{11111.6}.15625^{11111}}\)

Xét \(N=\frac{2020}{-66666^{55555}.11111^{11111}}\):

=> \(N=\frac{-2020}{\left(11111.6\right)^{11111.5}.11111^{11111}}\)

=> \(N=\frac{-2020}{11111^{11111.5}.6^{11111.5}.11111^{11111}}\)

=> \(N=\frac{-2020}{11111^{11111.5}.11111^{11111}.6^{11111.5}}\)

=> \(N=\frac{-2020}{11111^{11111.5+}^{11111}.6^{11111.5}}\)

=> \(N=\frac{-2020}{11111^{11111.6}.6^{11111.5}}\)

=> \(N=\frac{-2020}{11111^{11111.6}.7776^{11111}}\)

Vì 7776¹¹¹¹¹ < 15625¹¹¹¹¹ nên \(M=\frac{-2020}{11111^{11111.6}.15625^{11111}}\)> \(N=\frac{-2020}{11111^{11111.6}.7776^{11111}}\)

Vậy M > N

Answer 2

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Cảm ơn a ạ!