tìm x,y,z biết 3x=5y-7,4(y-2)=3(z-3) và 2x+3y-4z=2
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minh lam cau b) roi dc co 2/3 thoy ban tham khao nhe phan () la minh giai thich nha dung viet vo bai !!
2x=3y ; 5y = 7z
+) 10x=15y=21z ( Quy dong)
+)10x/210 = 15y/210 = 21z/210 ( BC)
+) x/21 = y/14 = z/10 ( Rut gon)
+) 3x/63 = 7y/98 = 5z/50 = 3x-7y+ 5z / 63 - 98 - 50 = -30/14 = -2
+ x/21 = 2 => ............ phan nay minh chua xong neu xong thi minh pm not cho
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\(a,4x=5y\:\Rightarrow\frac{x}{5}=\frac{y}{4}\Rightarrow\frac{x}{15}=\frac{y}{12}\)
\(4y=6z\Rightarrow\frac{y}{6}=\frac{z}{4}\Rightarrow\frac{y}{12}=\frac{z}{8}\)
\(\Rightarrow\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)
\(\Rightarrow\frac{x}{15}=\frac{2y}{24}=\frac{3z}{24}\)
\(\Rightarrow\frac{x-2y+3z}{15-24+24}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)
\(\Rightarrow\frac{5}{15}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)
\(\Rightarrow\frac{1}{3}=\frac{x}{15}=\frac{y}{12}=\frac{z}{8}\)
\(\Rightarrow\hept{\begin{cases}x=\frac{1}{3}\cdot15=5\\y=\frac{1}{3}\cdot12=4\\z=\frac{1}{3}\cdot8=\frac{8}{3}\end{cases}}\)
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a: \(\Leftrightarrow-15x+10=-7x+14\)
=>-8x=4
hay x=-1/2
\(a,\dfrac{2-3x}{x-2}=-\dfrac{7}{5}\left(x\ne2\right)\\ \Leftrightarrow14-7x=10-15x\\ \Leftrightarrow8x=-4\Leftrightarrow x=-2\left(tm\right)\\ c,\Leftrightarrow\dfrac{x-1}{2}=\dfrac{y-2}{5}=\dfrac{z-3}{4}=\dfrac{2x-2+3y-6-z+3}{2\cdot2+5\cdot3-4}=\dfrac{45}{15}=3\\ \Leftrightarrow\left\{{}\begin{matrix}x-1=6\\y-2=15\\z-3=12\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=7\\y=17\\z=15\end{matrix}\right.\\ d,\Leftrightarrow\dfrac{x}{1}=\dfrac{y}{3};\dfrac{y}{4}=\dfrac{z}{5}\\ \Leftrightarrow\dfrac{x}{4}=\dfrac{y}{12}=\dfrac{z}{15}=\dfrac{6x+7y+8z}{24+84+120}=\dfrac{456}{228}=2\\ \Leftrightarrow\left\{{}\begin{matrix}x=8\\y=24\\z=30\end{matrix}\right.\)
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\(\frac{2x-4y}{3}=\frac{4z-3x}{2}=\frac{3y-2z}{4}.\)VÀ \(2x-y+z=27\)
\(\frac{2x-4y}{3}=\frac{4z-3x}{2}=\frac{3y-2z}{4}=\frac{6x-12y}{9}\)\(=\frac{8z-6x}{4}=\frac{12y-8z}{16}\)
\(=\frac{6x-12y+8z-6x+12y-8z}{9+4+16}\)\(=\frac{0}{29}=0\)
\(\Rightarrow2x=4y\Rightarrow\frac{x}{4}=\frac{y}{2}\)
\(\Rightarrow4z=3x\Rightarrow\frac{z}{3}=\frac{x}{4}\)
\(\Rightarrow\frac{x}{4}=\frac{y}{2}=\frac{z}{3}\)
ÁP DỤNG TÍNH CHẤT CỦA DÃY TỈ SỐ BẰNG NHAU TA CÓ:
\(\frac{x}{4}=\frac{y}{2}=\frac{z}{3}=\frac{2x-y+z}{8-2+3}\)\(=\frac{27}{9}=3\)
\(\frac{x}{4}=3\Rightarrow x=12\)
\(\frac{y}{2}=3\Rightarrow y=6\)
\(\frac{z}{3}=3\Rightarrow z=9\)
VẬY X = 12, Y = 6, Z = 9