Question

1 .Tìm x , y , z biết rằng :

\(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}\) và x + y + z = 49

2.Thực hịên phép tính :

\(2^3+3\times\left(\dfrac{1}{2}\right)^2-\dfrac{1}{2^2}+\text{[}\left(-2\right)^2:\dfrac{1}{2}\times8\)

Giúp mik vs , cần gấp lắm .

Answer 1

Bài 1 :

Đặt :

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

\(\Leftrightarrow\left\{{}\begin{matrix}2x=3k\\3y=4k\\4z=5k\end{matrix}\right.\) \(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3k}{2}\\y=\dfrac{4k}{3}\\z=\dfrac{5k}{4}\end{matrix}\right.\)

Thay vào \(x+y+z=49\) ta được :

\(\dfrac{3k}{2}=\dfrac{4k}{3}=\dfrac{5k}{4}=49\)

\(\Leftrightarrow\dfrac{18k+16k+15k}{12}=\dfrac{588}{12}\)

\(\Leftrightarrow49k=588\)

\(\Leftrightarrow k=12\)

\(\Leftrightarrow\left\{{}\begin{matrix}x=\dfrac{3.12}{2}=18\\y=\dfrac{4.12}{3}=16\\z=\dfrac{5.12}{4}=15\end{matrix}\right.\)

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Answer 2

Bài1:

Từ \(\dfrac{2x}{3}=\dfrac{3y}{4}=\dfrac{4z}{5}=\dfrac{x}{90}=\dfrac{y}{80}=\dfrac{z}{75}\)

Áp dụng t/c của dãy tỉ số bằng nhau,ta có:

\(\dfrac{x}{90}=\dfrac{y}{80}=\dfrac{z}{75}=\dfrac{x+y+z}{90+80+75}=\dfrac{49}{245}=\dfrac{1}{5}\)

=>x=18;b=16;c=15

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