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\(B=\dfrac{\dfrac{2ab}{3}-\dfrac{3ab}{2}}{-\dfrac{5bb}{6}}\)
\(=\dfrac{\dfrac{4ab}{6}-\dfrac{9ab}{6}}{-\dfrac{5bb}{6}}\)
\(=\dfrac{-\dfrac{5ab}{6}}{-\dfrac{5bb}{6}}=\dfrac{ab.\dfrac{5}{6}}{bb.\dfrac{5}{6}}\)
\(=\dfrac{ab}{bb}=\dfrac{a}{b}\)
Với \(a=\dfrac{2021}{2022};b=\dfrac{2023}{2022}\), ta được:
\(B=\dfrac{2021}{2022}:\dfrac{2023}{2022}=\dfrac{2021}{2022}.\dfrac{2022}{2023}=\dfrac{2021}{2023}\)
\(P=\dfrac{a}{b+c}+\dfrac{b}{a+c}+\dfrac{c}{a+b}\\ \Rightarrow P+3=\left(\dfrac{a}{b+c}+1\right)+\left(\dfrac{b}{a+c}+1\right)+\left(\dfrac{c}{a+b}+1\right)\\ \Rightarrow P+3=\dfrac{a+b+c}{b+c}+\dfrac{a+b+c}{a+c}+\dfrac{a+b+c}{a+b}\\ =\left(a+b+c\right)\left(\dfrac{1}{b+c}+\dfrac{1}{a+c}+\dfrac{1}{a+b}\right)=2018.\dfrac{2021}{4034}=1011.000992\\ \Rightarrow P=1008.000992\)
\(\dfrac{4}{x}-\dfrac{y}{3}=\dfrac{1}{6}\)
\(\Rightarrow\dfrac{4}{x}-\dfrac{2y}{6}=\dfrac{1}{6}\)
\(\Rightarrow\dfrac{4}{x}=\dfrac{1}{6}+\dfrac{2y}{6}\)
\(\Rightarrow\dfrac{4}{x}=\dfrac{1+2y}{6}\)
\(\Rightarrow24=x\left(1+2y\right)\)
\(\Rightarrow x;1+2y\inƯ\left(24\right)\)
\(Ư\left(24\right)=\left\{\pm1;\pm2;\pm3;\pm4;\pm6;\pm8;\pm12;\pm24\right\}\)
Mà 1+2y lẻ nên:
\(\left\{{}\begin{matrix}1+2y=1\Rightarrow2y=0\Rightarrow y=0\\x=24\\1+2y=-1\Rightarrow2y=-2\Rightarrow y=-1\\x=-24\end{matrix}\right.\)
\(\left\{{}\begin{matrix}1+2y=3\Rightarrow2y=2\Rightarrow y=1\\x=8\\1+2y=-3\Rightarrow2y=-4\Rightarrow y=-2\\x=-8\end{matrix}\right.\)
\(a-b=11\)
\(P=\dfrac{5a-b}{4a+11}+\dfrac{5b-a}{4b-11}=\dfrac{5a-b}{4a+a-b}+\dfrac{5b-a}{4b-\left(a-b\right)}\)
\(=\dfrac{5a-b}{5a-b}+\dfrac{5b-a}{5b-a}\)
\(=2\)
Vậy...
a) Ta có:
2A=2.(12+122+123+...+122020+122021)2�=2.12+122+123+...+122 020+122 021
2A=1+12+122+123+...+122019+1220202�=1+12+122+123+...+122 019+122 020
Suy ra: 2A−A=(1+12+122+123+...+122019+122020)2�−�=1+12+122+123+...+122 019+122 020
−(12+122+123+...+122020+122021)−12+122+123+...+122 020+122 021
Do đó A=1−122021<1�=1−122021<1.
Lại có B=13+14+15+1360=20+15+12+1360=6060=1�=13+14+15+1360=20+15+12+1360=6060=1.
Vậy A < B.
Giải:
Ta có: \(\dfrac{a}{b}=\dfrac{-2}{3}\Rightarrow\dfrac{a}{-2}=\dfrac{b}{3}\)
Đặt \(\dfrac{a}{-2}=\dfrac{b}{3}=k\Rightarrow\left\{{}\begin{matrix}a=-2k\\b=3k\end{matrix}\right.\)
\(M=\dfrac{5a+2b}{3a-4b}=\dfrac{-10k+6k}{-6k-12k}=\dfrac{-4k}{-18k}=\dfrac{2}{9}\)
Vậy \(M=\dfrac{2}{9}\)
Từ \(\dfrac{a}{b}=\dfrac{-2}{3}\Rightarrow\dfrac{a}{-2}=\dfrac{b}{3}\)
Đặt \(\dfrac{a}{-2}=\dfrac{b}{3}=k\)
\(\Rightarrow a=-2k\) ; \(b=3k\)
Thay a=-2k và b = 3k vào M , ta có :
\(\dfrac{5.\left(-2\right)k+2.3k}{3.\left(-2\right)k-3.3k}=\dfrac{-10k+6k}{-6k-9k}=\dfrac{k\left(-10+6\right)}{k\left(-6-9\right)}=\dfrac{-4}{-15}=\dfrac{4}{15}\)Vậy...
\(A=\dfrac{3\cdot\dfrac{a}{b}-\dfrac{-a}{b}}{-\dfrac{-5a}{b}+\dfrac{4a}{b}}\\ =\left(\dfrac{3a}{b}+\dfrac{a}{b}\right):\left(\dfrac{5a}{b}+\dfrac{4a}{b}\right)\\ =\dfrac{4a}{b}:\dfrac{9a}{b}\\ =\dfrac{4a}{b}\cdot\dfrac{b}{9a}\\ =\dfrac{4}{9}\)
Vậy `a=2021/2022` ; `b=2023/2022` thì `A=4/9`
Thanks ạ