Question

[Kirigaya Kazuto]

So sánh A và B :

a) \(A=\dfrac{20}{39}+\dfrac{22}{27}+\dfrac{18}{43}\)

\(B=\dfrac{14}{39}+\dfrac{22}{29}+\dfrac{18}{41}\)

b) \(A=\dfrac{3}{8^3}+\dfrac{7}{8^4}\)

\(B=\dfrac{7}{8^3}+\dfrac{3}{8^4}\)

c) \(A=\dfrac{10^7+5}{10^7-8}\)

\(B=\dfrac{10^8+6}{10^8-7}\)

d) \(A=\dfrac{10^{1992}+1}{10^{1991}+1}\)

\(B=\dfrac{10^{1993}+1}{10^{1992}+1}\)

Answer 1

[Nguyễn Quang Ngọc Trác]

d, Vì B=10^1993+1/10^1992+1 > 1 =>10^1993+1/10^1992+1>10^1993+1+9/10^1992+1+9 = 10^1993+10/10^1992+10= 10. (10^1992+1)/10. (10^1991+1) = 10^1992+1/10^1991+1=A Vậy A=B

Answer 2

[Trèo lên cột điện thế hiện tình yêu]

cau d B>1 ta co tinh chat (\(\dfrac{a}{b}>\dfrac{a+m}{b+m}\) ) B> \(\dfrac{10^{1993}+1+9}{10^{1992}+1+9}\)\(=\dfrac{10^{1993}+10}{10^{1992}+10}\)=\(\dfrac{10\left(10^{1992}+1\right)}{10\left(10^{1991}+1\right)}\)=\(\dfrac{10^{1992}+1}{10^{1991}+1}\)=A

Suy ra B>A(chuc ban hoc goi nhe)