\(\dfrac{3a-2b}{5}=\dfrac{2c-5a}{3}=\dfrac{5b-3c}{2}=\dfrac{6c-15a}{9}=\dfrac{10b-6c}{4}=\dfrac{6c-15a+10b-6c}{9+4}=\dfrac{10b-15a}{13}\)
\(\Rightarrow\dfrac{3a-2b}{5}=\dfrac{10b-15a}{13}\Rightarrow39a-26b=50b-75a\)
\(\Rightarrow114a=76b\Rightarrow b=\dfrac{3}{2}a\)
Tương tự:
\(\dfrac{2c-5a}{3}=\dfrac{3a-2b}{5}=\dfrac{5b-3c}{2}=\dfrac{15a-10b}{25}=\dfrac{10b-6c}{4}=\dfrac{15a-10b+10b-6c}{25+4}=\dfrac{15a-6c}{29}\)
\(\Rightarrow\dfrac{2c-5a}{3}=\dfrac{15a-6c}{29}\Rightarrow58c-145a=45a-18c\)
\(\Rightarrow76c=190a\Rightarrow c=\dfrac{5}{2}a\)
Thế vào \(a^2+275=bc\)
\(\Rightarrow a^2+275=\left(\dfrac{3}{2}a\right).\left(\dfrac{5}{2}a\right)=\dfrac{15}{4}a^2\)
\(\Rightarrow\dfrac{11}{4}a^2=275\Rightarrow a^2=100\Rightarrow a=\pm10\)
- Với \(a=10\Rightarrow b=\dfrac{3}{2}a=15\) ; \(c=\dfrac{5}{2}a=25\)
- Với \(a=-10\Rightarrow b=-15;c=-25\)