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Áp dụng tính chất dãy tỉ số bằng nhau ta có :0
\(\dfrac{a_1-1}{9}=\dfrac{a_2-2}{8}=..............=\dfrac{a_9-9}{1}=\dfrac{\left(a_1+a_2+......+a_9\right)-\left(1+2+....+9\right)}{9+8+..+1}\)
\(=\dfrac{90-45}{45}=1\)
+) \(\dfrac{a_1-1}{9}=1\Leftrightarrow a_1=10\)
+) \(\dfrac{a_2-1}{8}=1\Leftrightarrow a_2=10\)
........................
+) \(\dfrac{a_9-9}{1}=1\Leftrightarrow a_9=10\)
Vậy \(a_1=a_2=..........=a_9=10\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{a_1-1}{9}=\dfrac{a_2-2}{8}=\dfrac{a_3-3}{7}=...=\dfrac{a_9-9}{1}\)
\(=\dfrac{a_1+a_2+...+a_9-\left(1+2+...+9\right)}{9+8+7+...+1}\)\(=\dfrac{90-45}{45}=1\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a_1-1}{9}=1\\\dfrac{a_2-2}{8}=1\\.................\\\dfrac{a_9-9}{1}=1\end{matrix}\right.\)\(\Rightarrow\left\{{}\begin{matrix}a_1-1=9\\a_2-2=8\\.................\\a_9-9=1\end{matrix}\right.\)\(\Rightarrow a_1=a_2=...=a_9=10\)
Với mọi x thuộc R Có (x^2-9)^2 \(\ge\) 0
[y-4] \(\ge\) 0
Suy ra (x^2-9)^2+[y-4] - 1 \(\ge\) -1
Xét A=-1 khi và chỉ khi (x^2-9)^2 và [y-4] đều bằng 0
Tự tính ra
Xin lỗi nhưng vì không biết nên mình phải dùng [ ] thay cho GTTĐ nhé
Xin lỗi nhiều tại mình o tìm được kí hiệu đó
Áp dụng tính chất dãy tỉ số bằng nhau ta có
\(\dfrac{x+y}{5}=\dfrac{x-y}{8}=\dfrac{x+y+x-y}{5+8}=\dfrac{2x}{13}=\dfrac{4x}{26}\)
Ta có:
\(\dfrac{x+y}{5}=\dfrac{xy}{26};\dfrac{x+y}{5}=\dfrac{4x}{26}\\ \Rightarrow\dfrac{xy}{26}=\dfrac{4x}{26}\Rightarrow y=4\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có
\(\dfrac{x+y}{5}=\dfrac{x-y}{8}=\dfrac{x+y-x+y}{5-8}=\dfrac{2y}{-3}\)
Ta có:
\(\dfrac{x-y}{8}=\dfrac{xy}{26};\dfrac{x-y}{8}=\dfrac{2y}{-3}\\ \Rightarrow\dfrac{xy}{26}=\dfrac{2y}{-3}\Rightarrow-3xy=52y\Leftrightarrow-3x=52\Rightarrow x=\dfrac{-52}{3}\)
Vậy \(x=-\dfrac{52}{3};y=4\)
\(\dfrac{3}{7}-x=\dfrac{1}{4}-\left(-\dfrac{3}{5}\right)\)
\(\Rightarrow\dfrac{3}{7}-x=\dfrac{17}{20}\)
\(\Rightarrow x=\dfrac{-59}{140}\)
Vậy \(x=\dfrac{-59}{140}.\)
Lần sau tự làm mấy bài này đi bạn
\(\dfrac{-3}{26}+2\dfrac{4}{69}=\dfrac{-3}{26}+2+\dfrac{4}{69}=\left(\dfrac{-3}{26}+\dfrac{4}{69}\right)+2=\dfrac{-103}{1794}+2=1,9425...\)
Máy mk ko quy đổi được về phân số bạn thông cảm trần thị anh thư
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=k\Rightarrow a=2k;b=3k;c=4k\\ \dfrac{2k}{2}=\dfrac{3k}{3}=\dfrac{4k}{4}\\ \Rightarrow\dfrac{\left(2k\right)^2}{2^2}=\dfrac{\left(3k\right)^2}{3^2}=\dfrac{2\left(4k\right)^2}{2\cdot4^2}\\ \Leftrightarrow\dfrac{4k^2}{4}=\dfrac{9k^2}{9}=\dfrac{32k^2}{32}=\dfrac{4k^2-9k^2+32k^2}{4-9+32}=\dfrac{108}{27}=4\\ \dfrac{4k^2-9k^2+32k^2}{4-9+32}=4\\ \Rightarrow\dfrac{\left(4-9+32\right)k^2}{4-9+32}=4\Rightarrow k^2=4\Rightarrow\left[{}\begin{matrix}k=2\\k=-2\end{matrix}\right.\\ k=2\Rightarrow\left\{{}\begin{matrix}a=2k=2\cdot2=4\\b=3k=3\cdot2=6\\c=4k=4\cdot2=8\end{matrix}\right.\\ k=-2\Rightarrow\left\{{}\begin{matrix}a=2k=2\cdot\left(-2\right)=-4\\b=3k=3\cdot\left(-2\right)=-6\\c=4k=4\cdot\left(-2\right)=-8\end{matrix}\right.\)
Vậy ...
Ta có : \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\)
Áp dụng t/c dãy tỉ số bằng nhau có :
\(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{a^2}{4}=\dfrac{b^2}{9}=\dfrac{c^2}{16}=\dfrac{a^2-b^2+2c^2}{4-9+32}=\dfrac{108}{27}=4\)
\(\Rightarrow\left[{}\begin{matrix}\dfrac{a}{2}=4\\\dfrac{b}{3}=4\\\dfrac{c}{4}=4\end{matrix}\right.\Rightarrow\left[{}\begin{matrix}a=8\\b=12\\c=16\end{matrix}\right.\)
6.(\(\dfrac{-2}{3}\))+12.\(\dfrac{-2^2}{3}\)+18.\(\dfrac{-2^3}{3}\)
= -4+(-16)+(-48)
=-68
>> Mình không chép lại đề bài nhé ! <<
Cách 1 :
\(A=\left(\dfrac{36-4+3}{6}\right)-\left(\dfrac{30+10-9}{6}\right)-\left(\dfrac{18-14+15}{6}\right)=\dfrac{35}{6}-\dfrac{31}{6}-\dfrac{19}{6}=-\dfrac{15}{6}=-\dfrac{5}{2}\)
Cách 2 :
\(A=6-\dfrac{2}{3}+\dfrac{1}{2}-5+\dfrac{5}{3}-\dfrac{3}{2}-3-\dfrac{7}{3}+\dfrac{5}{2}\)
\(A=\left(6-5-3\right)-\left(\dfrac{2}{3}+\dfrac{5}{3}-\dfrac{7}{3}\right)+\left(\dfrac{1}{2}+\dfrac{3}{2}-\dfrac{5}{2}\right)\)
\(A=-2-0-\dfrac{1}{2}=-\dfrac{5}{2}\)
Cách 1 :
\(\left(6-\dfrac{2}{3}+\dfrac{1}{2}\right)-\left(5+\dfrac{5}{3}-\dfrac{3}{2}\right)-\left(3-\dfrac{7}{3}+\dfrac{5}{2}\right)\)
\(=\left(\dfrac{36}{6}-\dfrac{4}{6}+\dfrac{3}{6}\right)-\left(\dfrac{30}{6}+\dfrac{10}{6}-\dfrac{9}{6}\right)-\left(\dfrac{18}{6}-\dfrac{14}{6}+\dfrac{15}{6}\right)\)
\(=\dfrac{35}{6}-\dfrac{31}{6}-\dfrac{19}{6}\)
\(=-\dfrac{5}{2}\)
Cách 2 :
\(\left(6-\dfrac{2}{3}+\dfrac{1}{2}\right)-\left(5+\dfrac{5}{3}-\dfrac{3}{2}\right)-\left(3-\dfrac{7}{3}+\dfrac{5}{2}\right)\)
\(=6-\dfrac{2}{3}+\dfrac{1}{2}-5-\dfrac{5}{3}+\dfrac{3}{2}-3+\dfrac{7}{3}-\dfrac{5}{2}\)
\(=\left(6-5-3\right)+\left(\dfrac{-2}{3}+\dfrac{-5}{3}+\dfrac{7}{3}\right)+\left(\dfrac{1}{2}+\dfrac{3}{2}+\dfrac{-5}{2}\right)\)
\(=\left(-2\right)+0+\dfrac{-1}{2}\)
\(=\dfrac{-5}{2}\)
M=\(\dfrac{3}{1^2.2^2}+\dfrac{5}{2^2.3^2}+\dfrac{7}{3^2.4^2}+...+\dfrac{17}{8^2.9^2}+\dfrac{19}{9^2.10^2}\)
=\(\dfrac{3}{1.4}+\dfrac{5}{4.9}+\dfrac{7}{9.16}+...+\dfrac{17}{64.81}+\dfrac{19}{81.100}\)
=\(1-\dfrac{1}{4}+\dfrac{1}{4}-\dfrac{1}{9}+\dfrac{1}{9}-\dfrac{1}{16}+...+\dfrac{1}{64}-\dfrac{1}{81}+\dfrac{1}{81}-\dfrac{1}{100}\)
=1-\(\dfrac{1}{100}\)=\(\dfrac{99}{100}\)<\(\dfrac{100}{100}=1\)
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