Question

[nguyen hoang phuong anh]

tính x, y, z biết

a) \(\dfrac{x}{2}=\dfrac{y}{3},\dfrac{y}{5}=\dfrac{z}{7}\), x + y + z = 92

b) 2x = 3y = 5z, x + y - z = 95

c) \(\dfrac{x}{y+x+1}=\dfrac{y}{x+z+1}=\dfrac{z}{x+y-2}=x+y+z\)

Answer 1

[Nguyễn Thanh Hằng]

a/ Ta có ;

\(x+y+z=92\)

\(\dfrac{x}{2}=\dfrac{y}{3};\dfrac{y}{5}=\dfrac{z}{7}\)

\(\Leftrightarrow\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{21}\)

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

\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{21}=\dfrac{x+y+z}{10+15+21}=\dfrac{92}{46}=2\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{10}=2\Leftrightarrow x=20\\\dfrac{y}{15}=2\Leftrightarrow y=30\\\dfrac{z}{21}=2\Leftrightarrow z=42\end{matrix}\right.\)

Vậy .................

b/Ta có :

\(x+y-z=95\)

\(2x=3y=5z\)

\(\Leftrightarrow\dfrac{2x}{30}=\dfrac{3y}{30}=\dfrac{5z}{30}\)

\(\Leftrightarrow\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{5}\)

Áp dụng t/x dãy tỉ số bằng nhau ta có :

\(\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{5}=\dfrac{x+y-z}{15+10-5}=\dfrac{95}{19}=5\)

\(\Leftrightarrow\left\{{}\begin{matrix}\dfrac{x}{15}=5\Leftrightarrow x=75\\\dfrac{y}{10}=5\Leftrightarrow y=50\\\dfrac{z}{5}=5\Leftrightarrow z=25\end{matrix}\right.\)

Vậy ..

Answer 2

[Trần Thị Hương]

a, \(\dfrac{x}{2}=\dfrac{y}{3},\dfrac{y}{5}=\dfrac{z}{7},x+y+z=92\)

Ta có: \(\dfrac{x}{2}=\dfrac{y}{3}\Leftrightarrow\dfrac{x}{10}=\dfrac{y}{15}\left(1\right)\)

\(\dfrac{y}{5}=\dfrac{z}{7}\Leftrightarrow\dfrac{y}{15}=\dfrac{z}{21}\left(2\right)\)

Từ (1) và (2) \(\Rightarrow\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{21},x+y+z=92\)

AD t/c DTS = nhau ta có:

\(\dfrac{x}{10}=\dfrac{y}{15}=\dfrac{z}{21}=\dfrac{x+y+z}{10+15+21}=\dfrac{92}{46}=2\)

+) \(\dfrac{x}{10}=2\Rightarrow x=20\)

+) \(\dfrac{y}{15}=2\Rightarrow y=30\)

+) \(\dfrac{z}{21}=2\Rightarrow z=42\)

b, \(2x=3y=5z,x+y-z=95\)

\(\Rightarrow\dfrac{30x}{15}=\dfrac{30y}{10}=\dfrac{30z}{6}\Rightarrow\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{6},x+y-z=95\)

AD t/c DTS = nhau ta có:

\(\dfrac{x}{15}=\dfrac{y}{10}=\dfrac{z}{6}=\dfrac{x+y-z}{15+10-6}=\dfrac{95}{19}=5\)

+) \(\dfrac{x}{15}=5\Rightarrow x=75\)

+) \(\dfrac{y}{10}=5\Rightarrow y=50\)

+) \(\dfrac{z}{6}=5\Rightarrow z=30\)

c, Bn xem lại đề bài nha!