Question

Tìm các số x,y,z biết rằng:  \(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\)và\(x+y+z=-7\)

 

Answer 1

\(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}=>\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{3}}=\frac{z}{\frac{5}{4}}\)

Áp dụng tính chất của dãy tỉ số bằng nhau ta có:

\(\frac{x}{\frac{3}{2}}=\frac{y}{\frac{4}{3}}=\frac{z}{\frac{5}{4}}=\frac{x+y+z}{\frac{3}{2}+\frac{4}{3}+\frac{5}{4}}=\frac{-7}{\frac{49}{12}}=-\frac{12}{7}\)

=>\(x=-\frac{12}{7}.\frac{3}{2}=-\frac{18}{7}\)

\(y=-\frac{12}{7}.\frac{4}{3}=-\frac{16}{7}\)

\(z=-\frac{12}{7}.\frac{5}{4}=-\frac{15}{7}\)

Answer 2

\(\frac{2x+3y+4z}{3+4+5}=\frac{-7}{12}\)

=> 2x/3=-7=>x= -21

=>3y/4=-7=>y=-28

=>4z/5= -7=> z= -35

tick bạn

Answer 3

\(\frac{2x}{3}=\frac{3y}{4}=\frac{4z}{5}\)

=> \(60.\frac{2x}{3}=60.\frac{3y}{4}=60.\frac{4z}{5}\)

=> \(\frac{120x}{3}=\frac{180y}{4}=\frac{240z}{5}=>40x=45y=48z\)

=> \(\frac{40x}{720}=\frac{45y}{720}=\frac{48z}{720}\)

=> \(\frac{x}{18}=\frac{y}{16}=\frac{z}{15}=\frac{x+y+z}{18+16+15}=\frac{-7}{49}=\frac{-1}{7}\)

=> x= -18/7

y= -16/7

z= -15/7

Answer 4

32x​=43y​=54z​

=> 60.\frac{2x}{3}=60.\frac{3y}{4}=60.\frac{4z}{5}60.32x​=60.43y​=60.54z​

=> \frac{120x}{3}=\frac{180y}{4}=\frac{240z}{5}=>40x=45y=48z3120x​=4180y​=5240z​=>40x=45y=48z

=> \frac{40x}{720}=\frac{45y}{720}=\frac{48z}{720}72040x​=72045y​=72048z​

=> \frac{x}{18}=\frac{y}{16}=\frac{z}{15}=\frac{x+y+z}{18+16+15}=\frac{-7}{49}=\frac{-1}{7}18x​=16y​=15z​=18+16+15x+y+z​=49−7​=7−1​

=> x= -18/7

y= -16/7

z= -15/7