[Toán 12] Hàm số mũ và lôgarit

N

nguyenbahiep1

mũ 3 cả 2 vế

[TEX] VT = \sqrt{3^3} + 3.\sqrt{3^2}.\sqrt[3]{30} + 3.\sqrt{3}.\sqrt[3]{30^2} + \sqrt[3]{30^3} \\ VP = 63[/TEX]

vậy ta chỉ cần so sánh

[TEX]\sqrt{3^3} + 3.\sqrt{3^2}.\sqrt[3]{30} + 3.\sqrt{3}.\sqrt[3]{30^2}[/TEX] với 33

ta có

[TEX]\sqrt{3^3} + 3.\sqrt{3^2}.\sqrt[3]{30} + 3.\sqrt{3}.\sqrt[3]{30^2} = \sqrt{27} + 9.\sqrt[3]{30} + 3.\sqrt{3}.\sqrt[3]{900} \\ \sqrt{27} > 5 \\ 9.\sqrt[3]{30} > 9.3 \\ 3.\sqrt{3}.\sqrt[3]{900} > 3.1.9 \\ \sqrt{27} + 9.\sqrt[3]{30} + 3.\sqrt{3}.\sqrt[3]{900} > 59 > 33[/TEX]

vậy

[TEX]\sqrt{3} + \sqrt[3]{30} > \sqrt[3]{63}[/TEX]
 
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