Question

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{6}\) và 3x-2y+2x= 24 Tìm x,y biết

Answer 1

Vì \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{6}\Rightarrow\dfrac{3x}{6}=\dfrac{2y}{6}=\dfrac{2z}{12}\)

Áp dụng tc dãy tỉ số bằng nhau ta có:

\(\dfrac{3x}{6}=\dfrac{2y}{6}=\dfrac{2z}{12}=\dfrac{3x-2y+2z}{6-6+ 12}=2\)

Do \(\dfrac{3x}{6}=2\Rightarrow x=4\)

\(\dfrac{2y}{6}=2\Rightarrow y=6\)

\(\dfrac{2z}{12}=2\Rightarrow z=12\)

Vậy \(x=4;y=6;z=12.\)

Answer 2

ta có: \(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{6}và3x-2y+2z=24\)

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

\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{6}=\dfrac{3x}{6}=\dfrac{2y}{6}=\dfrac{2z}{12}=\dfrac{3x-2y+2z}{6-6+12}=\dfrac{24}{12}=2\)

\(\dfrac{3x}{6}=2\Rightarrow3x=2.6=12\Rightarrow x=\dfrac{12}{3}=4\)

\(\dfrac{2y}{6}=2\Rightarrow2y=2.6=12\Rightarrow y=\dfrac{12}{2}=6\)

\(\dfrac{2z}{12}=2\Rightarrow2z=2.12=24\Rightarrow z=\dfrac{24}{2}=12\)

Vậy..............

Answer 3

Theo tính chất dãy tỉ số bằng nhau, ta có:
\(\dfrac{x}{2}=\dfrac{y}{3}=\dfrac{z}{6}=\dfrac{3x}{6}=\dfrac{2y}{6}=\dfrac{2z}{12}=\dfrac{3x-2y+2z}{6+6+12}=\dfrac{24}{24}=1\)
=> x = 2.1 = 2
y = 3.1 = 3
z = 6.1 = 6