b) Vì \(\hept{\begin{cases}2a=3b\\4b=5c\end{cases}}\Rightarrow\hept{\begin{cases}\frac{a}{3}=\frac{b}{2}\\\frac{b}{5}=\frac{c}{4}\end{cases}}\)  \(\Rightarrow\hept{\begin{cases}\frac{a}{15}=\frac{b}{10}\\\frac{b}{10}=\frac{c}{8}\end{cases}}\Rightarrow\frac{a}{15}=\frac{b}{10}=\frac{c}{8}\)

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

\(\frac{a}{15}=\frac{b}{10}=\frac{c}{8}=\frac{2a}{30}=\frac{2c}{16}=\frac{2a-b-2c}{30-10-16}=\frac{4}{4}=1\)

\(\Rightarrow\hept{\begin{cases}a=15\\b=10\\c=8\end{cases}}\)

Câu 5 :

Vì \(\hept{\begin{cases}a=2b\\b=3c\end{cases}}\Rightarrow\hept{\begin{cases}\frac{a}{2}=\frac{b}{1}\\\frac{b}{3}=\frac{c}{1}\end{cases}}\)\(\Rightarrow\hept{\begin{cases}\frac{a}{6}=\frac{b}{3}\\\frac{b}{3}=\frac{c}{1}\end{cases}}\Rightarrow\frac{a}{6}=\frac{b}{3}=\frac{c}{1}\)

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

\(\frac{a}{6}=\frac{b}{3}=\frac{c}{1}=\frac{2b}{6}=\frac{3c}{3}=\frac{a-2b+3c}{6-6+3}=\frac{6}{3}=2\)

\(\Rightarrow\hept{\begin{cases}a=2.6=12\\b=2.3=6\\c=2.1=2\end{cases}}\)

\(a,\hept{\begin{cases}a=2b\\b=3c\\a-2b+3c=6\end{cases}}\)

\(a-a+b=6\)

\(b=6\)

\(\Rightarrow\hept{\begin{cases}a=2b=2.6=12\\b=3c=3.6=18\end{cases}}\)

Vậy ... 

\(b,\hept{\begin{cases}2a=3b\\4b=5c\\2a-b-2c=4\end{cases}}\)

\(\hept{\begin{cases}2a=3b\\4b=5c\end{cases}}\Leftrightarrow\hept{\begin{cases}\frac{a}{3}=\frac{b}{2}\\\frac{b}{5}=\frac{c}{4}\end{cases}}\)

\(\Rightarrow\hept{\begin{cases}\frac{a}{15}=\frac{b}{10}\\\frac{b}{10}=\frac{c}{8}\end{cases}}\Rightarrow\frac{a}{15}=\frac{b}{10}=\frac{c}{8}\)

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

\(\frac{a}{15}=\frac{b}{10}=\frac{c}{8}=\frac{2a-b-2c}{2.15-10-2.8}=\frac{4}{4}=1\)

\(\Rightarrow\hept{\begin{cases}\frac{a}{15}=1\Rightarrow a=15\\\frac{b}{10}=1\Rightarrow b=10\\\frac{c}{8}=1\Rightarrow c=8\end{cases}}\)

c) Vì \(\hept{\begin{cases}\frac{3}{4}a=\frac{6}{5}b\\b\frac{2}{3}a=\frac{4}{7}c\end{cases}}\)\(\Rightarrow\hept{\begin{cases}\frac{3}{4}a=\frac{6}{5}b\\\frac{3}{4}a=\frac{9}{14}c\end{cases}}\Rightarrow\frac{3a}{4}=\frac{6b}{5}=\frac{9c}{14}\)

\(\Rightarrow\frac{a}{24}=\frac{b}{15}=\frac{c}{42}\)

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

\(\frac{a}{24}=\frac{b}{15}=\frac{c}{42}=\frac{c-b-a}{42-24-15}=\frac{11}{3}\)

\(\Rightarrow\hept{\begin{cases}a=\frac{11}{3}.24=88\\b=\frac{11}{3}.15=55\\c=\frac{11}{3}.42=154\end{cases}}\)

Câu 4 :

\(a,4x=5y\Rightarrow\frac{x}{5}=\frac{y}{4}\)

Đặt : 

\(\frac{x}{5}=\frac{y}{4}=k\)

\(\Rightarrow\hept{\begin{cases}x=5k\\y=4k\end{cases}}\)

Lại có : 

\(xy=80\)

\(5k.4k=80\)

\(20k^2=80\)

\(k^2=4\)

\(k=\pm2\)

\(\Rightarrow\hept{\begin{cases}x=5k=\pm10\\y=4k=\pm8\end{cases}}\)

Câu 4 :

Vì \(4x=5y\Rightarrow\frac{x}{5}=\frac{y}{4}\)\(\Rightarrow\left(\frac{x}{5}\right)^2=\frac{x}{5}.\frac{y}{4}=\left(\frac{y}{4}\right)^2\)

\(\Rightarrow\left(\frac{x}{5}\right)^2=\frac{x.y}{5.4}=\left(\frac{y}{4}\right)^2\)\(\Rightarrow\frac{x^2}{25}=\frac{80}{20}=4=\frac{y^2}{16}\)

\(\Rightarrow\hept{\begin{cases}x^2=4.25=100\\y^2=4.16=64\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=\pm10\\y=\pm8\end{cases}}\)

c) Vì \(\frac{x}{2}=\frac{y}{3}=\frac{z}{5}\)\(\Rightarrow\left(\frac{x}{2}\right)^2=\left(\frac{y}{3}\right)^2=\left(\frac{z}{5}\right)^2\)

\(\Rightarrow\frac{x^2}{2^2}=\frac{y^2}{3^2}=\frac{z^2}{5^2}\)\(\Rightarrow\frac{x^2}{4}=\frac{y^2}{9}=\frac{z^2}{25}\)

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

\(\frac{x^2}{4}=\frac{y^2}{9}=\frac{z^2}{25}=\frac{x^2+y^2+z^2}{4+9+25}=\frac{152}{38}=4\)

\(\Rightarrow\hept{\begin{cases}x^2=4.4=16\\y^2=4.9=36\\z^2=4.25=100\end{cases}}\)\(\Rightarrow\hept{\begin{cases}x=±4\\y=±6\\z=±10\end{cases}}\)

Sửa đề : d) \(\hept{\begin{cases}2x=4b=5c\\a^2-2b^2-3c^2=18\end{cases}}\)

d) Vì \(\hept{\begin{cases}2a=4b\\4b=5c\end{cases}}\Rightarrow\hept{\begin{cases}\frac{a}{4}=\frac{b}{2}\\\frac{b}{5}=\frac{c}{4}\end{cases}}\)\(\Rightarrow\hept{\begin{cases}\frac{a}{20}=\frac{b}{10}\\\frac{b}{10}=\frac{c}{8}\end{cases}}\Rightarrow\frac{a}{20}=\frac{b}{10}=\frac{c}{8}\)

\(\Rightarrow\left(\frac{a}{20}\right)^2=\left(\frac{b}{10}\right)^2=\left(\frac{c}{8}\right)^2\)\(\Rightarrow\frac{a^2}{20^2}=\frac{b^2}{10^2}=\frac{c^2}{8^2}\)

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

\(\frac{a^2}{20^2}=\frac{b^2}{10^2}=\frac{c^2}{8^2}=\frac{2b^2}{2.10^2}=\frac{3c^2}{3.8^2}=\frac{2b^2}{200}=\frac{3c^2}{192}=\frac{a^2-2b^2-2c^2}{20^2-200-192}=\frac{18}{8}=\frac{9}{4}=\left(\pm\frac{3}{2}\right)^2\)

\(\Rightarrow\hept{\begin{cases}a^2=\left(\pm\frac{3}{2}\right)^2.20^2=\left(\pm30\right)^2\\b^2=\left(±\frac{3}{2}\right)^2.10^2=\left(\pm15\right)^2\\c^2=\left(±\frac{3}{2}\right)^2.8^2=\left(±12\right)^2\end{cases}}\)

Mình vội quá nên thiếu

Phần d bài 4 bạn suy ra \(\hept{\begin{cases}a=±30\\b=±15\\c=±12\end{cases}}\)