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\(\dfrac{x+16}{9}=\dfrac{y-25}{-16}=\dfrac{z+49}{25}\) (1)
Ta có: \(4x^3-3=29\)
\(\Rightarrow4x^3=32\Rightarrow x^3=8\)
\(\Rightarrow x=2\)
Thay \(x=2\) vào điều (1) ta có:
\(\dfrac{2+16}{9}=\dfrac{y-25}{-16}=\dfrac{z+49}{25}\)
\(\Rightarrow\dfrac{y-25}{-16}=\dfrac{z+49}{25}=\dfrac{18}{9}\)
\(\Rightarrow\dfrac{y-25}{-16}=\dfrac{z+49}{25}=2\)
\(\Rightarrow\left\{{}\begin{matrix}y-25=2.\left(-16\right)\\z+49=2.25\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}y-25=-32\\z+49=50\end{matrix}\right.\)
\(\Rightarrow\left\{{}\begin{matrix}y=-7\\z=1\end{matrix}\right.\)
Vậy giá trị của biểu thức \(A=x+2y+3z\) là:
\(A=2+2.\left(-7\right)+3.1=2-14+3=-9\)
Chúc bạn học tốt!!!
Ta có : \(4x^3-3=29\)
\(\Rightarrow4x^3=32\)
\(\Rightarrow x^3=8\)
\(\Rightarrow x=2\)
Thay x = 2 vào \(\dfrac{x+16}{9}=\dfrac{y-25}{-16}\) ta có :
\(\dfrac{2+16}{9}=\dfrac{y-25}{-16}\)
\(\Rightarrow2=\dfrac{y-25}{-16}\)
\(\Rightarrow y-25=-32\)
\(\Rightarrow y=-7\)
Thay \(y=-7\) vào \(\dfrac{y-25}{-16}=\dfrac{z+49}{25}\) ta có :
\(\dfrac{-7-25}{-16}=\dfrac{z+49}{25}\)
\(\Rightarrow2=\dfrac{z+49}{25}\)
\(\Rightarrow z+49=50\)
\(\Rightarrow z=1\)
Thay x = 2; y = -7; z = 1 vào biểu thức A ta có :
\(A=2+2.\left(-7\right)+3.1\)
\(A=-9\)
Vậy A = -9
\(4x^3-3=29\\ \Rightarrow4x^3=32\\ \Rightarrow x^3=8\\ \Rightarrow x=2\)
\(\dfrac{x+16}{9}=\dfrac{2+16}{9}=2\\\Rightarrow\dfrac{y-15}{-16}=\dfrac{z+49}{25}=2\\ \Rightarrow\left\{{}\begin{matrix}y-15=2.\left(-16\right)=-32\\z+49=2.25=50\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}y=-17\\z=1\end{matrix}\right.\)
\(4x^3-3=29\Rightarrow x^3=\dfrac{29+3}{4}=8\Rightarrow x=\sqrt[3]{8}=2\)
Thay số: \(\dfrac{x+16}{9}=\dfrac{2+16}{9}=2\)
Suy ra: \(y=\left(-16\right)\cdot2+25\Leftrightarrow y=-7\) và \(z=25\cdot2-49\Leftrightarrow z=1\)
\(A=x+2y+3z\Leftrightarrow2+\left(-14\right)+3=-9\)
\(4x^3-3=29\Rightarrow x^3=\dfrac{32}{4}=2^3\Rightarrow x=3\)
\(\dfrac{19}{9}=\dfrac{2y-2.25}{-32}=\dfrac{3z+49.3}{75}=\dfrac{2y+3z+49.3-25.2}{75-32}=\dfrac{2y+3z+97}{43}\)
\(\dfrac{\left(2y+3z+3\right)+94}{43}=\dfrac{19}{9}\) \(\Rightarrow\left(x+2y+3z\right)=\dfrac{43.19}{9}-94\)
\(B=\dfrac{1}{99\cdot97}-\dfrac{1}{97\cdot95}-\dfrac{1}{95\cdot93}-...-\dfrac{1}{3\cdot1}\)
\(B=-\left(\dfrac{1}{3\cdot1}+\dfrac{1}{5\cdot3}+...+\dfrac{1}{97\cdot99}\right)\)
\(2B=-\left(\dfrac{2}{3\cdot1}+\dfrac{2}{5\cdot3}+...+\dfrac{2}{99\cdot97}\right)\)
\(2B=-\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{97}-\dfrac{1}{99}\right)\)
\(2B=-\left(1-\dfrac{1}{99}\right)\)
\(2B=-\dfrac{98}{99}\)
\(B=-\dfrac{98}{198}\)
Cậu ơi, \(\dfrac{1}{99\cdot97}\) là dương mà sao lại đưa vào ngoặc âm tất cả vậy nhỉ?
Ta có:\(\dfrac{x^2}{4}=\dfrac{x}{2};\dfrac{y^2}{9}=\dfrac{y}{3};\dfrac{z^2}{25}=\dfrac{z}{5}\)
Aps dụng tính chất dãy tỉ số bằn nhau:
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{x-y+z}{2-3+5}=\dfrac{4}{4}=1\)
=>\(\dfrac{x}{2}=1=>x=2\)
\(\dfrac{y}{3}=1=>y=3\)
\(\dfrac{z}{5}=1=>z=5\)
Vậy x=2, y=3, z=5
Ta có : \(\dfrac{x^2}{4}=\dfrac{y^2}{9}=\dfrac{z^2}{25}\Rightarrow\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta được :
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{x-y+z}{2-3+5}=\dfrac{4}{4}=1\)
\(\Leftrightarrow x=2;y=3;z=5\)
a: =11/7(-3/7+4/11-4/7+7/11)=0
b: \(=\dfrac{1}{99\cdot97}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{95}-\dfrac{1}{97}\right)\)
\(=\dfrac{1}{99\cdot97}-\dfrac{1}{2}\cdot\dfrac{96}{97}=\dfrac{1}{99\cdot97}-\dfrac{48}{97}=-\dfrac{4751}{9603}\)
Mình sửa lại chút.
\(\dfrac{1}{99.97}-\dfrac{1}{97.95}-\dfrac{1}{95.93}-\dfrac{1}{5.3}-\dfrac{1}{3.1}\)
\(=\dfrac{1}{99.97}-\left\{\dfrac{1}{97.95}+\dfrac{1}{95.93}\right\}-\left\{\dfrac{1}{5.3}+\dfrac{1}{3.1}\right\}\)
\(=\dfrac{1}{99.97}-\dfrac{1}{95}.\left\{\dfrac{1}{97}+\dfrac{1}{93}\right\}-\dfrac{1}{3}.\left\{\dfrac{1}{5}+\dfrac{1}{1}\right\}\)
\(=\dfrac{1}{99.97}-\dfrac{1}{95}.\dfrac{190}{97.93}-\dfrac{1}{3}.\dfrac{6}{5}\)
\(=\dfrac{1}{99.97}-\dfrac{2}{97.93}-\dfrac{6}{15}\)
\(=\dfrac{1}{97}.\left\{\dfrac{1}{99}-\dfrac{2}{93}\right\}-\dfrac{2}{5}\)
\(=\dfrac{-35}{297693}-\dfrac{2}{5}\)
\(=\dfrac{-175-595386}{1488465}\)
\(=\dfrac{-595561}{1488465}\)
Bài 1:
\(\dfrac{1}{99.97}-\dfrac{1}{97.95}-\dfrac{1}{95.93}-...-\dfrac{1}{5.3}-\dfrac{1}{3.1}\)
\(=\dfrac{1}{99.97}-\left(\dfrac{1}{1.3}+\dfrac{1}{3.5}+...+\dfrac{1}{93.95}+\dfrac{1}{95.97}\right)\)
\(=\dfrac{1}{99.97}-\dfrac{1}{2}\left(\dfrac{2}{1.3}+\dfrac{2}{3.5}+...+\dfrac{2}{93.95}+\dfrac{2}{95.97}\right)\)
\(=\dfrac{1}{97.99}-\dfrac{1}{2}\left(1-\dfrac{1}{3}+\dfrac{1}{3}-\dfrac{1}{5}+...+\dfrac{1}{93}-\dfrac{1}{95}+\dfrac{1}{95}-\dfrac{1}{97}\right)\)
\(=\dfrac{1}{97.99}-\dfrac{1}{2}\left(1-\dfrac{1}{97}\right)\)
\(=\dfrac{1}{97.99}-\dfrac{1}{2}.\dfrac{96}{97}\)
\(=\dfrac{1}{97.99}-\dfrac{48}{97}\)
Bạn tính nốt nhé
Bài 2, 3 bạn kiểm tra lại đề giúp mk
Bài 1 :
\(\dfrac{1}{99.97}-\dfrac{1}{99.95}-\dfrac{1}{95.93}-......-\dfrac{1}{5.3}-\dfrac{1}{3.1}\)
\(=\dfrac{1}{97.99}-\left(\dfrac{1}{97.95}+\dfrac{1}{95.93}+...+\dfrac{1}{5.3}-\dfrac{1}{3.1}\right)\)
\(=\dfrac{1}{97.99}-\dfrac{1}{2}\left(\dfrac{1}{95}-\dfrac{1}{97}+\dfrac{1}{93}-\dfrac{1}{95}+...+\dfrac{1}{3}-\dfrac{1}{5}+1-\dfrac{1}{3}\right)\)
\(=\dfrac{1}{97.99}-\dfrac{1}{2}\left(1-\dfrac{1}{97}\right)\)
\(=\dfrac{1}{97.99}-\dfrac{48}{97}\)
\(=\dfrac{51}{97}\)