Ta có:
\(a=3b=4c=5d\)
\(\Rightarrow\dfrac{a}{60}=\dfrac{3b}{60}=\dfrac{4c}{60}=\dfrac{5d}{60}\)
\(\Rightarrow\dfrac{a}{60}=\dfrac{b}{20}=\dfrac{c}{15}=\dfrac{d}{12}\)
\(\Leftrightarrow\dfrac{ab}{1200}=\dfrac{c^2}{255}=\dfrac{d^2}{144}\)
Áp dụng tính chất dãy tỉ số bằng nhau ta có:
\(\dfrac{ab}{1200}=\dfrac{c^2}{255}=\dfrac{d^2}{144}=\dfrac{ab-c^2-d^2}{1200-255-144}=\dfrac{831}{831}\)
\(\Leftrightarrow\dfrac{d^2}{144}=\dfrac{831}{831}\Rightarrow d^2=\dfrac{144.831}{831}=144\Rightarrow d=\pm12\)
Ta có hai trường hợp:
Nếu \(d=12\) \(\Rightarrow\left\{{}\begin{matrix}b=20\\c=15\end{matrix}\right.\) \(\Rightarrow b-c=5\)
Nếu \(d=-12\) \(\Rightarrow\left\{{}\begin{matrix}b=-20\\c=-15\end{matrix}\right.\) \(\Rightarrow b-c=-5\)
Vậy \(b-c=\pm5\)
