Question

a, x/6=y/-5=z/4 và 2x+y=21

b, x/y=9/10; y/z=3/4 và x-y-z=43

c, x/3=y/4 và x*y=192

Answer 1

a) \(\dfrac{x}{6}=\dfrac{y}{-5}=\dfrac{z}{4}\rightarrow\dfrac{z}{4}=\dfrac{2x}{12}=\dfrac{y}{-5}=\dfrac{2x+y}{12-5}=\dfrac{21}{7}=3\)

-Suy ra: x=6.3=18; y=(-5).3=-15; z=4.3=12

Answer 2

b) \(\dfrac{x}{y}=\dfrac{9}{10}\rightarrow\dfrac{x}{9}=\dfrac{y}{10}\rightarrow\dfrac{x}{27}=\dfrac{y}{30}\)

\(\dfrac{y}{z}=\dfrac{3}{4}\rightarrow\dfrac{z}{4}=\dfrac{y}{3}\rightarrow\dfrac{z}{40}=\dfrac{y}{30}\)

\(\rightarrow\dfrac{x}{27}=\dfrac{y}{30}=\dfrac{z}{40}=\dfrac{x-y-z}{27-30-40}=\dfrac{43}{43}=1\)

\(\rightarrow x=27;y=30;z=40\)

Answer 3

c) \(\dfrac{x}{3}=\dfrac{y}{4}=k\rightarrow x=3k;y=4k\)

x.y=192\(\rightarrow3k.4k=192\rightarrow k^2=\dfrac{192}{12}\rightarrow k^2=16\rightarrow k=\pm4\)

-Khi k=4 suy ra x=3k=12 và y=4k=16

-Khi k=-4 suy ra x=3k=-12 và y=4k=-16