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tử số : 2.4 + 4.8 + 8.12 + 12.16 + 16.20
= 2.(1.2+2.4+4.6+6.8+8.10)
ta được 2. A=( 1.2+2.4+4.6+6.8+8.10) / ( 1.2+2.4+4.6+6.8+8.10)
=> A=2
\(A=\frac{8056}{2012.16-1982}\)= \(\frac{2014.4}{2012.15+2012-1982}\)=\(\frac{2014.4}{2012.15+30}\)=\(\frac{2014.4}{2012.15+2.15}\)=\(\frac{2014.4}{15.\left(2012+2\right)}=\frac{2014.4}{15.2014}=\frac{4}{15}\)
B = \(\frac{1.2.6+2.4.12+4.8.24+7.14.42}{1.6.9+2.12.18+4.24.36+7.42.63}\)
= \(\frac{1.2.3.2+2.2.2.12+4.4.2.24+7.7.2.42}{1.2.3.9+2.12.2.9+4.24.4.9+7.42.7.9}\)
= \(\frac{2\left(1.2.3+2.2.12+4.4.24+7.7.42\right)}{9\left(1.2.3+2.2.12+4.4.24+7.7.42\right)}\)
= \(\frac{2}{9}\)
Ta có: \(\frac{4}{15}=\frac{4.3}{15.3}=\frac{12}{45};\frac{2}{9}=\frac{2.5}{9.5}=\frac{10}{45}\)
Vì \(\frac{12}{45}>\frac{10}{45}\Rightarrow\frac{4}{15}>\frac{2}{9}\Rightarrow A>B\)
Vậy A > B
\(A=\dfrac{8056}{2012.16-1982}\)
\(A=\dfrac{8056}{32192-1982}\)
\(A=\dfrac{8056}{30210}=\dfrac{12}{45}\)
\(B=\dfrac{1.2.6+2.4.12+4.8.24+7.14.42}{1.6.9+2.12.18+4.24.36+7.42.63}\)
\(B=\dfrac{12+96+768+4116}{54+432+3456+18522}\)
\(B=\dfrac{4992}{22464}=\dfrac{10}{45}\)
Vậy: \(\dfrac{12}{45}>\dfrac{10}{45}\Rightarrow A>B\)
\(\frac{2.4.10+4.6.8+14.16.20}{3.6.15+6.9.12+21.24.30}=\frac{2\left(1.2.5\right)+2\left(2.3.4\right)+2\left(7.8.9\right)}{3\left(1.2.5\right)+3\left(2.3.4\right)+3\left(7.8.9\right)}=\frac{2\left(1.2.5+2.3.4+7.8.9\right)}{3\left(1.2.5+2.3.4+7.8.9\right)}=\frac{2}{3}.\)
Hacker 2k6
Trả lời:
\(\frac{2.4.10+4.6.8+14.16.20}{3.6.15+6.9.12+21.24.30}\)
\(=\frac{2\left(1.2.5\right)+2\left(2.3.4\right)+2\left(7.8.10\right)}{3\left(1.2.5\right)+3\left(2.3.4\right)+3\left(7.8.10\right)}\)
\(=\frac{2\left(1.2.5+2.3.4+7.8.10\right)}{3\left(1.2.5+2.3.4+7.8.10\right)}\)
\(=\frac{2}{3}\)(Vì\(1.2.5+2.3.4+7.8.10\ne0\))
Hok tốt!
Good girl
\(\dfrac{1\cdot2\cdot3+2\cdot4\cdot6+4\cdot8\cdot12}{1\cdot3\cdot5+2\cdot6\cdot10+4\cdot12\cdot20}\\ =\dfrac{1\cdot2\cdot3+2\cdot1\cdot2\cdot2\cdot2\cdot3+4\cdot1\cdot4\cdot2\cdot4\cdot3}{1\cdot3\cdot5+2\cdot1\cdot2\cdot3\cdot2\cdot5+4\cdot1\cdot4\cdot3\cdot4\cdot5}\\ =\dfrac{1\cdot2\cdot3\cdot\left(1+2^3+4^3\right)}{1\cdot3\cdot5\cdot\left(1+2^3+4^3\right)}\\ =\dfrac{1\cdot2\cdot3}{1\cdot3\cdot5}\\ =\dfrac{6}{15}\)
Tách phần lử trên ra sao cho có thể rút gọn với phần ơn dưới
\(=\dfrac{8+8\cdot8+8\cdot64+8\cdot512}{12+12\cdot8+12\cdot64+12\cdot512}=\dfrac{8}{12}=\dfrac{2}{3}\)