Question

[Cô nàng cá tính]

Bài toán:

a, So sánh 3¹²⁵ và 4⁹³

b, So sánh không qua quy đồng

\(A=\frac{-7}{10^{2005}}+\frac{-15}{10^{2006}}\)

\(B=\frac{-15}{10^{2005}}+\frac{-7}{10^{2006}}\)

Ai làm nhanh mình tick cho

Answer 1

[Phùng Quang Thịnh]

a) Có \(3^{125}=3^{124}.3=\left(3^4\right)^{31}.3=81^{31}.3\)
\(4^{93}=\left(4^3\right)^{31}=64^{31}\)
Vì \(81^{31}>64^{31}\Rightarrow81^{31}.3>64^{31}\)
=) \(3^{125}>4^{93}\)
b) Có \(A=\frac{-7}{10^{2005}}+\frac{-15}{10^{2006}}=\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}\)
\(B=\frac{-15}{10^{2005}}+\frac{-7}{10^{2006}}=\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)
Vì \(\frac{-7}{10^{2005}}=\frac{-7}{10^{2005}},\frac{-7}{10^{2006}}=\frac{-7}{10^{2006}},\frac{-8}{10^{2006}}>\frac{-8}{10^{2005}}\)
=) \(\frac{-7}{10^{2005}}+\frac{-7}{10^{2006}}+\frac{-8}{10^{2006}}>\frac{-7}{10^{2005}}+\frac{-8}{10^{2005}}+\frac{-7}{10^{2006}}\)
=) A > B 

Answer 2

[uzumaki naruto]

a) Ta có: 3¹²⁴= (3⁴)³¹= 81³¹

4⁹³= (4³)³¹= 64 ³¹

Do 81³¹ >  64 ³¹ => 3¹²⁴ < 4⁹³ 

Mà 3¹²⁴< 3¹²⁵ => 3¹²⁵ > 4⁹³