Question

\(\dfrac{x}{3}=\dfrac{y}{7};x.y=84\)

Answer 1

\(\dfrac{x}{3}=\dfrac{y}{7};x.y=84\)

Đặt \(\dfrac{x}{3}=\dfrac{y}{7}=k\)

⇒ x = 3k ; y = 7k

⇒ x . y = 3k . 7k

⇒ 84 = 21 . k²

⇒ k² = \(\dfrac{84}{21}=4\)

⇒ k = \(\pm2\)

+ ) Nếu k = 2 ⇒ \(\left\{{}\begin{matrix}x=2.3=6\\y=2.7=14\end{matrix}\right.\)

+ ) Nếu k = -2 ⇒ \(\left\{{}\begin{matrix}x=-2.3=-6\\y=-2.7=-14\end{matrix}\right.\)

Vậy ( x , y ) ∈ { ( 6 , 14 ) ; (-6 , -14 ) }

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