Question

[Trâm Nguyễn]

Cho 2�−3�+�=422x−3y+z=42. Tìm �x; �y và �z sao cho �−3=�5−3x​=5y​ và �−2=�7−2y​=7z​.

�=3611x=1136​; �=−6011y=−1160​; �=21011z=11210​. �=3x=3; �=−5y=−5; �=21z=21. �=1811x=1118​; �=−33011y=−11330​; �=10511z=11105​. �=367x=736​; �=−607y=−760​; �=30z=30.

Answer 1

[HT.Phong (9A5)]

Ta có: \(-3x=5y\Rightarrow\dfrac{-3x}{15}=\dfrac{5y}{15}\Rightarrow\dfrac{x}{-5}=\dfrac{y}{3}\Rightarrow\dfrac{x}{35}=\dfrac{y}{-21}\)(1)

\(-2y=7z\Rightarrow\dfrac{-2y}{14}=\dfrac{7z}{14}\Rightarrow\dfrac{y}{-7}=\dfrac{z}{2}\Rightarrow\dfrac{y}{-21}=\dfrac{z}{6}\) (2) 

Từ (1) và (2) ta có: \(\dfrac{x}{35}=\dfrac{y}{-21}=\dfrac{z}{6}\)

Áp dụng tính chất dãy tỉ số bằng nhau ta có:

\(\dfrac{x}{35}=\dfrac{y}{-21}=\dfrac{z}{6}=\dfrac{2x-3y+z}{2\cdot35-3\cdot-21+6}=\dfrac{42}{139}\) 

\(\Rightarrow\dfrac{x}{35}=\dfrac{42}{139}\Rightarrow x=\dfrac{1470}{139}\)

\(\Rightarrow\dfrac{y}{-21}=\dfrac{42}{139}\Rightarrow y=-\dfrac{882}{139}\)

\(\Rightarrow\dfrac{z}{6}=\dfrac{42}{139}\Rightarrow z=\dfrac{252}{139}\) 

Answer 2

[Đàm Minh Quang]

giup mik vs