so sánh a=10^21-3/10^22-3 và b=10^20+1/10^21+1
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A = \(\dfrac{10^{20}+3}{10^{21^{ }}+3}\)
B = \(\dfrac{10^{21}+4}{10^{22}+4}\) < 1
\(\Rightarrow\) B < \(\dfrac{10^{21}+4+6}{10^{22}+4+6}\)
\(\Rightarrow\) B < \(\dfrac{10^{21}+10}{10^{22}+10}\)
\(\Rightarrow\) B < \(\dfrac{10\left(10^{20}+1\right)}{10\left(10^{21}+1\right)}\)
\(\Rightarrow\) B < \(\dfrac{10^{20}+1}{10^{21}+1}\) < \(\dfrac{10^{21}+1+2}{10^{22}+1+2}\)
\(\Rightarrow\) B < \(\dfrac{10^{21}+3}{10^{22}+3}\)
\(\Rightarrow\) B < A
\(A=\left(\frac{20}{5}+\frac{27}{9}\right)\times\frac{21}{10}=\left(4+3\right)\times\frac{21}{10}=7\times\frac{21}{10}=\frac{147}{10}\)
\(B=\left(\frac{13}{6}-\frac{3}{8}\right)\times\frac{11}{22}\)
\(B=\left(\frac{52}{24}-\frac{9}{24}\right)\times\frac{11}{22}\)
\(B=\frac{43}{24}\times\frac{1}{2}=\frac{43}{48}\)
Dễ thấy \(A=\frac{147}{10}>1\)
Mà \(B=\frac{43}{48}< 1\)
=> tự so sánh
Đặt A = \(\frac{10^{20}+1}{10^{21}+1}\)
=> 10A = \(\frac{10^{21}+10}{10^{21}+1}=1+\frac{9}{10^{21}+1}\)
Đặt B = \(\frac{10^{21}+1}{10^{22}+1}\)
=> 10B = \(\frac{10^{22}+10}{10^{22}+1}=1+\frac{9}{10^{22}+1}\)
Vì \(\frac{9}{10^{21}+1}>\frac{9}{10^{22}+1}\)
=> \(1+\frac{9}{10^{21}+1}>1+\frac{9}{10^{22}+1}\)
=> 10A > 10B
=> A > B
a) (x - 3)(y - 3) = 9 = 1.9 = 3.3
Lập bảng:
x - 3 | 1 | -1 | 3 | -3 | 9 | -9 |
y - 3 | 9 | -9 | 3 | -3 | 1 | -1 |
x | 4 | 2 | 6 | 0 | 12 | -3 |
y | 12 | -6 | 6 | 0 | 4 | 2 |
Vậy ...
b) A = \(\frac{10^{19}+1}{10^{20}+1}\) => 10A = \(\frac{10^{20}+10}{10^{20}+1}=1+\frac{9}{10^{20}+1}\)
B = \(\frac{10^{20}+1}{10^{21}+1}\) => 10B = \(\frac{10^{21}+10}{10^{21}+1}=1+\frac{9}{10^{21}+1}\)
Do \(10^{20}+1< 10^{21}+1\) => \(\frac{9}{10^{20}+1}>\frac{9}{10^{21}+1}\) => 10A > 10B => A > B
\(M=\dfrac{10^{20}+1}{10^{19}+1}\)
\(N=\dfrac{10^{21}+1}{10^{20}+1}< \dfrac{10^{21}+1+9}{10^{20}+1+9}=\dfrac{10^{21}+10}{10^{20}+10}=\dfrac{10\left(10^{20}+1\right)}{10\left(10^{19}+1\right)}=\dfrac{10^{20}+1}{10^{19}+1}=M\)
\(\Rightarrow N< M\)
M = \(\dfrac{10^{20}+1}{10^{19}+1}\) = 10 - \(\dfrac{9}{10^{19}+1}\) ; N = \(\dfrac{10^{21}+1}{10^{20}+1}\) = 10 - \(\dfrac{9}{10^{20}+1}\)
Vì \(\dfrac{9}{10^{19}+1}\) > \(\dfrac{9}{10^{20}+1}\)
⇒ M < N (phân số nào có phần bù lớn hơn thì phân số đó nhỏ hơn)
\(M=\dfrac{10^{20}+1}{10^{19}+1}\)
\(N=\dfrac{10^{21}+1}{10^{20}+1}< \dfrac{10^{21}+1+9}{10^{20}+1+9}=\dfrac{10^{21}+10}{10^{20}+10}=\dfrac{10\left(10^{20}+1\right)}{10\left(10^{19}+1\right)}=\dfrac{10^{20}+1}{10^{19}+1}=M\)
\(\Rightarrow N< M\)
A Lớn hơn