Toán Lớp 6: so sánh phân số
A=10 mũ 15 +1 / 10 mũ 14 +1
b=10 mũ 13+1 / 10mux 12+1
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Toán Lớp 6: so sánh phân số
A=10 mũ 15 +1 / 10 mũ 14 +1
b=10 mũ 13+1 / 10mux 12+1
Comments ( 1 )
Giải đáp:
$A>B.$
Lời giải và giải thích chi tiết:
$A=\dfrac{10^{15}+1}{10^{14}+1}\\ =\dfrac{10^{15}+10-9}{10^{14}+1}\\ =\dfrac{10(10^{14}+1)-9}{10^{14}+1}\\ =\dfrac{10(10^{14}+1)}{10^{14}+1}-\dfrac{9}{10^{14}+1}\\ =10-\dfrac{9}{10^{14}+1}\\ B=\dfrac{10^{13}+1}{10^{12}+1}\\ =\dfrac{10^{13}+10-9}{10^{12}+1}\\ =\dfrac{10(10^{12}+1)-9}{10^{12}+1}\\ =\dfrac{10(10^{12}+1)}{10^{12}+1}-\dfrac{9}{10^{12}+1}\\ =10-\dfrac{9}{10^{12}+1}\\ 10^{14}>10^{12}\\ \Rightarrow 10^{14}+1>10^{12}+1\\ \Rightarrow \dfrac{9}{10^{14}+1}<\dfrac{9}{10^{12}+1}\\ \Rightarrow -\dfrac{9}{10^{14}+1}>-\dfrac{9}{10^{12}+1}\\ \Rightarrow 10-\dfrac{9}{10^{14}+1}>10-\dfrac{9}{10^{12}+1}\\ \Leftrightarrow A>B.$