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2x^3-1=15
=>2x^3=16
=>x=2
(x+16)/9=(y-5)/16=(z+9)/25
=>(y-5)/16=(z+9)/25=2
=>y-5=32 và z+9=50
=>y=37 và z=41
B=x+y+z=2+37+41=80
Ta có: \(2x^3-1=15\Leftrightarrow x^3=8\Rightarrow x=2\)
\(\Rightarrow\dfrac{18}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\Rightarrow\left\{{}\begin{matrix}\dfrac{y-25}{16}=2\Rightarrow y=57\\\dfrac{z+9}{25}=2\Rightarrow z=41\end{matrix}\right.\)
Vậy \(B=x+y+z=2+57+41=100\)
Cho \(\dfrac{x+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}và\dfrac{9-x}{7}+\dfrac{11-x}{9}=2\).Tìm x+y+z
theo bài ra ta có:
\(\dfrac{x+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\)
áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{x+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}=\dfrac{x+16+y-25+z+9}{9+16+25}=\dfrac{x+y+z}{50}\\ \Rightarrow\dfrac{x+16}{9}=\dfrac{x+y+z}{50}\left(1\right)\)ta lại có:
\(\dfrac{9-x}{7}+\dfrac{11-x}{9}=2\\ \Rightarrow\dfrac{7+2-x}{7}+\dfrac{9+2-x}{9}=2\\ \Rightarrow\left(1+\dfrac{2-x}{7}\right)+\left(1+\dfrac{2-x}{9}\right)=2\\ \Rightarrow\left(1+1\right)+\left(\dfrac{2-x}{7}+\dfrac{2-x}{9}\right)=2\\ \Rightarrow2+\left(2-x\right)\left(\dfrac{1}{7}+\dfrac{1}{9}\right)=2\\ \Rightarrow\left(2-x\right)\left(\dfrac{1}{7}+\dfrac{1}{9}\right)=0\\ \Rightarrow2-x=0\\ \Rightarrow x=2\)
thay x = 2 vào 1 ta có:
\(\Rightarrow\dfrac{2+16}{9}=\dfrac{x+y+z}{50}\\ \Rightarrow\dfrac{18}{9}=\dfrac{x+y+z}{50}\\ \Rightarrow2=\dfrac{x+y+z}{50}\\ \Rightarrow x+y+z=2.50\\ \Rightarrow x+y+z=100\)
vậy x + y + z = 100
b: 2x^3-1=15
=>2x^3=16
=>x=2
\(\dfrac{x+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\)
=>\(\dfrac{y-25}{16}=\dfrac{z+9}{25}=\dfrac{18}{9}=2\)
=>y-25=32; z+9=50
=>y=57; z=41
d: 3/5x=2/3y
=>9x=10y
=>x/10=y/9=k
=>x=10k; y=9k
x^2-y^2=38
=>100k^2-81k^2=38
=>19k^2=38
=>k^2=2
TH1: k=căn 2
=>\(x=10\sqrt{2};y=9\sqrt{2}\)
TH2: k=-căn 2
=>\(x=-10\sqrt{2};y=-9\sqrt{2}\)
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 :
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=\dfrac{x-y+z}{2-3+5}=\dfrac{4}{4}=1\)
\(\Leftrightarrow x=2;y=3;z=5\)
Ta có :
\(2x^3-1=15\)
\(\Leftrightarrow2x^3=16\)
\(\Leftrightarrow x^3=8\)
\(\Leftrightarrow x=2\)
Thay \(x=2\) zô : \(\dfrac{x+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\)
\(\Leftrightarrow\dfrac{2+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\)
\(\Leftrightarrow\dfrac{y-25}{16}=\dfrac{z+9}{25}=\dfrac{18}{9}=2\)
+) \(\dfrac{y-25}{16}=2\)
\(\Leftrightarrow y-25=32\)
\(\Leftrightarrow y=57\)
+) \(\dfrac{z+9}{25}=2\)
\(\Leftrightarrow z+9=50\)
\(\Leftrightarrow z=41\)
Ta có :
\(\left\{{}\begin{matrix}x=2\\y=57\\z=41\end{matrix}\right.\) \(\Leftrightarrow x+y+z=2+57+41=100\)
\(2x^3-1=15\)
\(\Rightarrow2x^3=16\)
\(\Rightarrow x^3=8\)
\(\Rightarrow x=2\)
Thay x vào \(\dfrac{x+16}{9}=\dfrac{y-25}{16}+\dfrac{z+9}{25}\) thì tìm được y và z
Tính nốt x + y + z
\(2x^3-1=15\)
\(2x^3=16\)
\(x^3=8\)
\(\Rightarrow x=2\)
\(\dfrac{x+16}{9}=\dfrac{y+25}{16}=\dfrac{z+9}{25}\)
\(\Leftrightarrow\dfrac{2+16}{9}=\dfrac{y-25}{16}=\dfrac{z+9}{25}\)
\(\Leftrightarrow\dfrac{y-25}{16}=\dfrac{z+9}{25}=\dfrac{18}{9}=2\)
\(\Rightarrow\dfrac{y-25}{16}=2\)
\(\Rightarrow y-25=32\)
\(\Rightarrow y=57\)
\(\Rightarrow\dfrac{z+9}{25}=2\)
\(\Rightarrow z+9=50\)
\(\Rightarrow z=41\)
\(\Rightarrow\)\(x=2\) , \(y=57\) , \(z=41.\)
\(B=x+y+z\)
\(B=2+57+41\)
\(B=100\)
Vậy \(B=100\)
2. Tham khảo thêm tại đây nha bạn
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