Question

x/2=y/3=z/5 và xyz=810

 

Answer 1

\(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}vs\left(x.y.x=810\right)\)

Đặt : \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=K\)

=> x=k.2

y=k.3

z=k.5

=> \(2k.3k.5k=810\)

\(\Rightarrow30k^3=810\)

\(\Rightarrow k^3=27\)

\(\Rightarrow k=\text{±3}\)

TH1 : k=3

=> x=3.2=6

y=3.3=9

x=3.5=15

TH2 : k=-3

=> x=-3.2=-6

y=-3.3=-9

x=-3.5=-15

Answer 2

Ta đặt \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}=k\)

\(\Rightarrow x=2k;y=3k;z=5k\)

\(\Rightarrow xyz=2k.3k.5k\)

\(\Rightarrow xyz=30.k^3\)

\(\Rightarrow810=30.k^3\)

\(\Rightarrow k^3=810:30=27\)

\(\Rightarrow k=3\)

Nên x = 3 x 2 = 6

       y = 3 x 3 = 9

       z = 3 x 5 = 15

Answer 3

Vì \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\Rightarrow\left(\frac{x}{2}\right)^3=\left(\frac{y}{3}\right)^3=\left(\frac{z}{5}\right)^3=\frac{x}{2}.\frac{y}{3}.\frac{z}{5}=\frac{zyz}{2.3.5}=\frac{810}{30}=27\)

\(\Rightarrow\frac{x^3}{2^3}=\frac{y^3}{3^3}=\frac{z^3}{5^3}=\left(±3\right)^3\)

\(\Rightarrow\hept{\begin{cases}x^3=\left(±3\right)^3.2^3=\left(±6\right)^3\\y^3=\left(±3\right)^3.3^3=\left(±9\right)^3\\z^3=\left(±3\right)^3.5^3=\left(±15\right)^3\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\pm6\\y=\pm9\\z=\pm15\end{cases}}\)

Mà x , y , z cùng dấu

=> ( x , y , z ) ∈ { ( -6 , -9 , -15 ) ; ( 6 , 9 , 15 ) }