Question

So sánh tổng A và tổng B biết rằng :

   \(A=\frac{2006}{987654321}+\frac{2007}{24681357}\) và   \(B=\frac{2006}{24681357}+\frac{2007}{987654321}\)

Answer 1

Quy đồng 

A=(2006.246813579+2007.987654321)/(246... 

B=(2007.246813579+2006.987654321)/(246... 

MS bằng nhau nên ta so sánh tử: 

A'=2006.246813579+2007.987654321=2006.... +987654321 

=2006.(246813579+987654321)+987654321 

B'=2007.246813579+2006.987654321 =2006.246813579+246813579+2006.987654321 

=2006.(246813579+987654321)+246813579 

987654321>246813579 

Nên A'>B' 

Hay A>B

Answer 2

ĐÁP ÁN :A>B

Answer 3

cách 2 : Ta co : 

987654321 * 246813579 * A = 2006 * 246813579 + 2007 * 987654321 (1) 

987654321 * 246813579 * B = 2007 * 246813579 + 2006 * 987654321 (2) 

Lay (1) tru (2) ta duoc : 

987654321 * 246813579 * (A - B) = 987654321 - 246813579 > 0 

---> A - B > 0 ---> A > B.

Answer 4

A= \(\frac{2006}{987654321}+\frac{2006}{24681357}+\frac{1}{24681357}\)

B=\(\frac{2006}{24681357}+\frac{2006}{987654321}+\frac{1}{987654321}\)

Vì \(\frac{1}{24681357}>\frac{1}{987654321}\) nên A>B