Đặt \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{5}=k\Rightarrow x=2k;y=3k;z=5k\)
Thay k vào xy+yz+zx=31 ta có :
xy+yz+zx=31
\(\Rightarrow2k\cdot3k+3k\cdot5k+5k\cdot2k=31\)
\(\Rightarrow6\cdot k^2+15\cdot k^2+10\cdot k^2=31\)
\(\Rightarrow k^2\left(6+15+10\right)=31\)
\(\Rightarrow k^2\cdot31=31\)
\(\Rightarrow k^2=1\)
\(\Rightarrow k\cdot k=1\cdot1\)
\(\Rightarrow k=1\)
Từ đó suy ra :
*x=2k=2
*y=3k=3
*z=5k=5
Vậy x=2,y=3,z=5
nhó tick mink nhé
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