Ta có: \(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)
\(\Rightarrow\) \(\frac{z-5}{6}=\frac{x-1}{2}=\frac{y+3}{4}\)
\(\Rightarrow\frac{5z-25}{30}=\frac{3x-3}{6}=\frac{4y+12}{16}=\frac{\left(5z-3x-4y\right)-25+3-12}{30-6-16}=\frac{50-34}{8}=\frac{16}{8}=2\)
\(\Rightarrow\)x = 5
y = 5
z = 17
x-1/2=y+3/4=z-5/6=k suy ra x-1=2k;y+3=4k;z-5=6k va x=2k+1;y=4k-3;z=6k+5
5(6k+5)-3(2k+1)-4(4k-3)=25+30k-3+6k-16k-12=(25-3-12)+(30k+6k-16k)
=10+20k=50 suy ra 20k=50-10=40 suy ra k=40:20=2
x=2.2+1=5
y=2.4-3=5
z=2.6+5=17
tìm x,y,z biết (x+y)2014+(2y+6)2016+|z+5|=0
\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}=a\)
\(x-1=2a\Rightarrow x=2a+1\)
\(y+3=4a\Rightarrow y=4a-3\)
\(z-5=6a\Rightarrow z=6a+5\)
\(5z-3x-4y=50\)
\(30a+25-6a-3-16a+12=50\)
\(8a+34=50\)
\(a=2\)
\(x=2a+1=5\)
\(y=4a-3=5\)
\(z=6a+5=17\)