Question

So sánh:

A = \(\dfrac{20^{10}+1}{20^{10}-1}\)

B = \(\dfrac{20^{10}-1}{20^{10}-3}\)

Answer 1

Ta có :

\(A=\dfrac{20^{10}+1}{20^{10}-1}=\dfrac{20^{10}-1+2}{20^{10}-1}=1+\dfrac{2}{20^{10}-1}\)

\(B=\dfrac{20^{10}-1}{20^{10}-3}=\dfrac{20^{10}-3+2}{20^{10}-3}=1+\dfrac{2}{20^{10}-3}\)

Vì \(1+\dfrac{2}{20^{10}-1}< 1+\dfrac{2}{20^{10}-3}\)

\(\Rightarrow A< B\)

~ Chúc bn học tốt~

Answer 2

\(A=\dfrac{20^{10}+1}{20^{10}-1}=\dfrac{20^{10}-1+2}{20^{10}-1}=1+\dfrac{2}{20^{10}-1}\) (1)

\(B=\dfrac{20^{10}-1}{20^{10}-3}=\dfrac{20^{10}-3+2}{20^{10}-3}=1+\dfrac{2}{20^{10}-3}\) (2)

vì \(20^{10}-1>20^{10}-3\)

nên \(\dfrac{2}{20^{10}-1}< \dfrac{2}{20^{10}-3}\) (3)

từ (1), (2) và (3) suy ra A<B

Answer 3

vì B>1

Suy ra B>\(\dfrac{20^{10}-1+2}{20^{10}-3+2}=\dfrac{20^{10}+1}{20^{10}-1}=A\)

Suy ra B>A

Answer 4

Ta co : A = 20^10+1/20^10-1= 20^10+2-1/20^10-1=20^10-1/20^10-1+2/20^10-1=1+2/20^10-1

B = 20^-1/20^10-3= 20^10-3+2/20^10-3= 20^10-3/20^10-3+2/20^10-3= 1+2/20^10-3

Vi 20^10-1>20^10-3(ma mau cang be thi phan so cang lon, mau cang lon thi phan so cang be)nén+2/20^10-1<1+2/20^10-3 hay A<B

Vay A<B