Question

Tìm x , y ,z biết\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}\)và 5z - 3x - 4y = 50

Answer 1

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

Answer 2

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

Answer 3

tìm x,y,z biết (x+y)²⁰¹⁴+(2y+6)²⁰¹⁶+|z+5|=0

Answer 4

\(\frac{x-1}{2}=\frac{y+3}{4}=\frac{z-5}{6}=a\)

\(x-1=2a\Rightarrow x=2a+1\)

\(y+3=4a\Rightarrow y=4a-3\)

\(z-5=6a\Rightarrow z=6a+5\)

\(5z-3x-4y=50\)

\(30a+25-6a-3-16a+12=50\)

\(8a+34=50\)

\(a=2\)

\(x=2a+1=5\)

\(y=4a-3=5\)

\(z=6a+5=17\)