Question

So sánh \(55^{66}\)và \(66^{55}\)

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Answer 1

Ta có : 55⁶⁶ = [(11.5)⁶]¹¹ = (11⁶ . 5⁶)¹¹ = (11⁵ . 11 . 5⁶)¹¹

66⁵⁵ = [(11.6)⁵]¹¹ = (11⁵ . 6⁵)¹¹

Vì 11 . 5⁶ > 6⁵ nên 55⁶⁶ > 66⁵⁵

Answer 2

\(55^{66}=\left(55^6\right)^{11}=\left[\left(11.5\right)^6\right]^{11}=\left(11^6.5^6\right)^{11}=\left(11^5.11.5^6\right)^{11}\)

\(66^{55}=\left(66^5\right)^{11}=\left[\left(11.6\right)^5\right]^{11}=\left(11^5.6^5\right)^{11}\)

Vì : \(11.5^6>6^5\)

Vậy : \(55^{66}>66^{55}\)