\(\frac{A^{2011+2012}}{A^{2012+2013}}\)VÀ\(\frac{A^{2011}}{A^{2012}}+\frac{A^{2012}}{A^{2013}}\)
So sánh
CHO : \(A=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
VÀ : \(B=\frac{2010+2011+2012}{2011+2012+2013}\)
SO SÁNH A VÀ B
TA CÓ :
\(B=\frac{2010+2011+2012}{2011+2012+2013}\)
\(B=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
VÌ : \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\)
=> A > B
VẬY , A > B
Mình tự hỏi. sao banh biết rồi còn đăng lên làm gì??????????
cho \(A=\frac{2011}{2012}+\frac{2012}{2013};B=\frac{2011+2013}{2012+2013}\)So sánh A và B
Gọi 2011 là a
2012 là b;2013 là c
=>\(A=\frac{2011}{2012}+\frac{2012}{2013}=\frac{a}{b}+\frac{b}{c}\);\(B=\frac{2011+2013}{2012+2013}=\frac{a+c}{b+c}\)
=>\(A=\frac{a}{b}+\frac{b}{c}=\frac{ac+b^2}{bc}\)\(=\frac{\left(ac+b^2\right).\left(b+c\right)}{bc.\left(b+c\right)}\);\(B=\frac{a+c}{b+c}=\frac{\left(a+c\right).bc}{bc.\left(b+c\right)}\)
b+c>a+c;b2+ac>bc
Vậy A>B
So sánh \(A=\frac{2011}{2012}+\frac{2012}{2013}\) và \(B=\frac{2011+2012}{2012+2013}\)
Ta có \(B=\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2013}+\frac{2012}{2013}=\frac{2011+2012}{2013}\)
Lại có: \(\frac{2011+2012}{2013}>\frac{2011+2012}{2012+2013}\) ( ngoặc 2 dòng này lại nhé dòng này và dòng trên)
\(\Rightarrow B>A\)
so sánh \(A=\frac{2011+2012}{2012+2013}vàB=\frac{2011}{2012}+\frac{2012}{2013}\)
\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}
Tách A ra thành 2 phân số cùng tử(dễ thôi).
So sánh mỗi phân số với 1 phân số tương ứng ở B.
=>A<B.
Vậy A<B.
So sánh \(A=\frac{2011}{2012}+\frac{2012}{2013}\) và \(B=\frac{2011+2012}{2012+2013}\)
ta có: \(\frac{2011}{2012}>\frac{2011}{2012+2013};\frac{2012}{2013}>\frac{2012}{2013+2012}.\)
\(\Rightarrow A>\frac{2011}{2012+2013}+\frac{2012}{2013+2012}=\frac{2011+2012}{2012+2013}=B\)
....
Ta có \(\frac{2011}{2012}>\frac{2011}{2012+2013}\)
\(\frac{2012}{2013}>\frac{2012}{2012+2013}\)
CỘNG VẾ THEO VẾ,TA CÓ:
\(\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)
\(\Rightarrow\frac{2011}{2012}+\frac{2012}{2013}>\frac{2011+2012}{2012+2013}\)
\(\Rightarrow A>B\)
Vậy A>B
So sánh: A=\(\frac{2011+2012}{2012+2013}\)và B=\(\frac{2011}{2012}+\frac{2012}{2013}\)
A=\(\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)
B=\(\frac{2011}{2012}+\frac{2012}{2013}\)
mà \(\frac{2011}{2012+2013}<\frac{2011}{2012};\frac{2012}{2012+2013}<\frac{2012}{2013}\)
nên A <B
a) So sánh P và Q
Biết\(P=\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\) và\(\frac{2010+2011+2012}{2011+2012+2013}\)
b) Tìm hai số tự nhiên a và b, biết: BCNN(a,b)=420;ƯCLN(a,b)=21 và a+21=b
Áp dụng BĐT \(\frac{a}{b}+\frac{b}{c}+\frac{c}{d}>\frac{a+b+c}{a+b+c}=1>\frac{a+b+c}{b+c+d}\).
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2010+2011+2012}>\frac{2010+2011+2012}{2011+2012+2013}\)mà 2010 + 2011 + 2012 < 2011+2012+2013 ,suy ra \(\frac{2010+2011+2012}{2011+2012+2013}< 1\))
\(\Rightarrow\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}>\frac{2010+2011+2012}{2011+2012+2013}\)hay P > Q
Vậy P > Q
b) Áp dụng công thức BCNN (a, b) . UCLN (a,b) = a.b
\(\Rightarrow a.b=420.21=8820\)
Ta có:
\(ab=8820\)
\(a+21=b\Rightarrow b-a=21\)
Hai số cách nhau 21 mà có tích là 8820 là 84 , 105
Mà a + 21 = b suy ra a < b
Vậy a = 84 ; b = 105
a,-Cách khác:
-Ta có: \(\frac{2010+2011+2012}{2011+2012+2013}=\frac{2010}{2011+2012+2013}+\frac{2011}{2011+2012+2013}+\frac{2012}{2011+2012+2013}\)
-Mà: \(\frac{2010}{2011}>\frac{2010}{2011+2012+2013}\left(1\right)\)
\(\frac{2011}{2012}>\frac{2011}{2011+2012+2013}\left(2\right)\)
\(\frac{2012}{2013}>\frac{2012}{2011+2012+2013}\left(3\right)\)
\(\Rightarrow P>Q\)
So sánh:
A=\(\frac{2010}{2011}+\frac{2011}{2012}+\frac{2012}{2013}\)
B=\(\frac{2010+2011+2012}{2011+2012+2013}\)
cậu tra trên mạng í lắm lắm
so sánh \(A=\frac{2011+2012}{2012+2013}\)\(B=\frac{2011}{2012}+\frac{2012}{2013}\)
ta có:\(\frac{2011+2012}{2012+2013}=\frac{2011}{2012+2013}+\frac{2012}{2012+2013}\)
vì \(\frac{2011}{2012+2013}<\frac{2011}{2012};\frac{2012}{2012+2013}<\frac{2012}{2013}\)
=>A<B