Tính M = 3\(\dfrac{1}{437}\) * \(\dfrac{1}{762}\) - \(\dfrac{1}{139}\) * 4\(\dfrac{761}{762}\) - \(\dfrac{4}{417\cdot762}\) + \(\dfrac{5}{139}\) .
Giúp mình giải chi tiết bài này nha, các bạn.
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\(M=\left(\dfrac{1252}{417.762}-\dfrac{4}{417.762}\right)-\left(\dfrac{1}{139}+\dfrac{5}{139}\right).\dfrac{3809}{762}\)
\(M=\left(\dfrac{1252-4}{317754}\right)-\dfrac{6}{139}.\dfrac{3809}{762}\)
\(M=\left(\dfrac{1248}{317754}\right)-\dfrac{22854}{105918}\)
\(M=\dfrac{208}{52959}-\dfrac{3809}{17653}\)
\(M=\dfrac{3671824}{934885227}-\dfrac{201720831}{934885227}\)
\(M=\dfrac{-198049007}{934885227}\)
\(A=3\dfrac{1}{417}.\dfrac{1}{762}-\dfrac{1}{139}+\dfrac{761}{762}-\dfrac{4}{417.762}+\dfrac{5}{139}\)
\(=\left(\dfrac{1252}{417.762}-\dfrac{4}{417.762}\right)+\left(-\dfrac{1}{139}+\dfrac{5}{139}\right)+\dfrac{761}{762}\)
\(=\dfrac{1248}{417.762}+\dfrac{4}{139}+\dfrac{761}{762}=\dfrac{1248}{417.672}+\dfrac{12.762}{417.762}+\dfrac{761.417}{417.762}\)
\(=\dfrac{327729}{317754}\)
Câu 2
(a+3)(b-4)-(a-3)(b+4)=0
=>ab-4a+3b-12-ab-4a+3b+12=0
=>-8a=-6b
=>a/b=3/4
=>a/3=b/4
Bài 2:
Giải:
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a_1-1}{9}=\dfrac{a_2-2}{8}=...=\dfrac{a_9-9}{1}=\dfrac{a_1-1+a_2-2+...+a_9-9}{9+8+...+1}=\dfrac{\left(a_1+a_2+...+a_9\right)-\left(1+2+...+9\right)}{9+8+...+1}\)
\(=\dfrac{90-45}{45}=1\)
+) \(\dfrac{a_1-1}{9}=1\Rightarrow a_1=10\)
+) \(\dfrac{a_2-2}{8}=1\Rightarrow a_2=10\)
...
+) \(\dfrac{a_9-9}{1}=1\Rightarrow a_9=10\)
Vậy \(a_1=a_2=...=a_9=10\)
Đặt 761=a; 139=b
\(M=\left(3+\dfrac{1}{3b}\right)\cdot\dfrac{1}{a+1}-\dfrac{1}{b}\cdot\left(4+\dfrac{a}{a+1}\right)-\dfrac{4}{\left(a+1\right)\cdot3b}+\dfrac{5}{b}\)
\(=\dfrac{9b+1}{3b}\cdot\dfrac{1}{a+1}-\dfrac{1}{b}\cdot\dfrac{4a+4}{a+1}-\dfrac{4}{3b\left(a+1\right)}+\dfrac{5}{b}\)
\(=\dfrac{9b+1-3\left(4a+4\right)-4+15\left(a+1\right)}{3b\left(a+1\right)}\)
\(=\dfrac{9b+1-12a-12-4+15a+15}{3b\left(a+1\right)}\)
\(=\dfrac{3a+9b}{3b\left(a+1\right)}=\dfrac{3\left(a+3b\right)}{3b\left(a+1\right)}=\dfrac{a+3b}{b\left(a+1\right)}\)
\(=\dfrac{761+3\cdot139}{139\left(761+1\right)}=\dfrac{589}{52959}\)