Question

Bài 3: Tìm x, y, z biết: 𝑥/3= 𝑦/2; 𝑦/3=𝑧/5 và x – y + z = 20

Answer 1

Ta có: 2x=y3=z52x=y3=z5

⇒x=y6=z25⇒x=y6=z25và x+y−z2=−20x+y−z2=−20

Áp dụng tính chất dãy tỉ số bằng nhau, ta được

x=y6=z25=x+y−z21+6−5=−202=−10x=y6=z25=x+y−z21+6−5=−202=−10(vìx+y−z2=−20x+y−z2=−20)

⇒\hept⎧⎨⎩x=−10y=−10⋅6=−60z2=−10⋅5=−50⇒\hept⎧⎨⎩x=−10y=−60z=−100

Answer 2

x2=y3=z5" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:18.56px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x2=y3=z5 và x2=y3=z5=x+y+z2+3+5=2010=2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:18.56px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x2=y3=z5=x+y+z2+3+5=2010=2

x2=2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:18.56px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">x2=2 y3=2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:18.56px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">y3=2 z5=2" role="presentation" style="border:0px; box-sizing:border-box; direction:ltr; display:inline-block; float:none; font-size:18.56px; line-height:0; margin:0px; max-height:none; max-width:none; min-height:0px; min-width:0px; overflow-wrap:normal; padding:1px 0px; position:relative; white-space:nowrap; word-break:break-word; word-spacing:normal" class="MathJax_CHTML mjx-chtml">z5=2 $\Rightarrow z=2.5=10$

Vậy $x=4$; $y=6$ và $z=10$.

Chúc bạn học tốt!

Answer 3

Ta có :

x - y + z = 20

\(\hept{\begin{cases}\frac{x}{3}=\frac{y}{2}\\\frac{y}{3}=\frac{z}{5}\end{cases}}\Rightarrow\hept{\begin{cases}\frac{x}{9}=\frac{y}{6}\\\frac{y}{6}=\frac{z}{10}\end{cases}}\Rightarrow\frac{x}{9}=\frac{y}{6}=\frac{z}{10}\)

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

\(\frac{x}{9}=\frac{y}{6}=\frac{z}{10}=\frac{x-y+z}{9-6+10}=\frac{20}{13}\)

\(\Rightarrow\hept{\begin{cases}x=\frac{20}{13}.9=\frac{180}{13}\\y=\frac{20}{13}.6=\frac{120}{13}\\z=\frac{20}{13}.10=\frac{200}{13}\end{cases}}\)

Answer 4

Từ : \(\frac{x}{3}=\frac{y}{2}\)\(\Rightarrow\)\(\frac{x}{3}.\frac{1}{3}=\frac{y}{2}.\frac{1}{3}=\frac{x}{9}=\frac{y}{6}\)( 1 )

Từ : \(\frac{y}{3}=\frac{z}{5}\)\(\Rightarrow\)\(\frac{y}{3}.\frac{1}{2}=\frac{z}{5}.\frac{1}{2}=\frac{y}{6}=\frac{z}{10}\)( 2 )

Từ ( 1 ) và ( 2 ) \(\Rightarrow\)\(\frac{x}{9}=\frac{y}{6}=\frac{z}{10}\)

Đặt \(\frac{x}{9}=\frac{y}{6}=\frac{z}{10}=k\)

\(\Rightarrow\hept{\begin{cases}x=9k\\y=6k\\z=10k\end{cases}}\)

Thay vào \(x-y+z=20\)ta có :

\(9k-6k+10k=20\)

\(13k=20\)

\(k=\frac{20}{13}\)

Thay vào ta được :

\(\Rightarrow\hept{\begin{cases}x=9.\frac{20}{13}\\y=6.\frac{20}{13}\\z=10.\frac{20}{13}\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\frac{180}{13}\\y=\frac{120}{13}\\z=\frac{200}{13}\end{cases}}\)