1) Ta có a:b:c:d = 2:3:4:5
\(\Rightarrow\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có: \(\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}=\dfrac{d}{5}=\dfrac{a+b+c+d}{2+3+4+5}=\dfrac{42}{14}=3\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{a}{2}=3\Rightarrow a=3.2=6\\\dfrac{b}{3}=3\Rightarrow b=3.3=9\\\dfrac{c}{4}=3\Rightarrow c=3.4=12\\\dfrac{d}{5}=3\Rightarrow d=3.5=15\end{matrix}\right.\)
Vậy a = 6, b = 9, c = 12, d = 15
2) Ta có: \(2x=3y\Rightarrow\dfrac{x}{3}=\dfrac{y}{2}\) (1)
Ta cũng có: \(5y=7z\Rightarrow\dfrac{y}{7}=\dfrac{z}{5}\) (2)
Từ (1) và (2) \(\Rightarrow\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có: \(\dfrac{x}{21}=\dfrac{y}{14}=\dfrac{z}{10}=\dfrac{3x-7y+5z}{3.21-7.14+5.10}=\dfrac{30}{15}=2\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x}{21}=2\Rightarrow x=2.21=42\\\dfrac{y}{14}=2\Rightarrow y=2.14=28\\\dfrac{z}{10}=2\Rightarrow z=2.10=20\end{matrix}\right.\)
Vậy x = 42, y = 28, z = 20
3) Ta có x:y:z = 4:5:6
\(\Rightarrow\dfrac{x}{4}=\dfrac{y}{5}=\dfrac{z}{6}\)
\(\Rightarrow\left(\dfrac{x}{4}\right)^2=\left(\dfrac{y}{5}\right)^2=\left(\dfrac{z}{6}\right)^2\)
\(\Rightarrow\dfrac{x^2}{16}=\dfrac{y^2}{25}=\dfrac{z^2}{36}\)
Áp dụng tính chất dãy tỉ số bằng nhau, ta có: \(\dfrac{x^2}{16}=\dfrac{y^2}{25}=\dfrac{z^2}{36}=\dfrac{x^2-2y^2+z^2}{16-2.25+36}=\dfrac{18}{2}=9\)
\(\Rightarrow\left\{{}\begin{matrix}\dfrac{x^2}{16}=9\Rightarrow\dfrac{x}{4}=3\Rightarrow x=3.4=12\\\dfrac{y^2}{25}=9\Rightarrow\dfrac{y}{5}=3\Rightarrow y=3.5=15\\\dfrac{z^2}{36}=9\Rightarrow\dfrac{z}{6}=3\Rightarrow x=3.6=18\end{matrix}\right.\)
Vậy x = 12, y = 15, z = 18
