Question

\(Tìm\) \(a,b,c\) \(biết\) \(:\)

\(a)\frac{a}{3}=\frac{b}{4}\) \(và\) \(a.b=48\)

\(b)\frac{a}{2}=\frac{b}{-3}\) \(và\) \(a.b=-54\)

\(c)\frac{a}{2}=\frac{b}{3}=\frac{c}{5}\) \(và\) \(a.b.c=810\)

Answer 1

Answer 2

a) Ta có: \(\frac{a}{3}=\frac{b}{4}.\)

=> \(\frac{a}{3}=\frac{b}{4}\) và \(a.b=48.\)

Đặt \(\frac{a}{3}=\frac{b}{4}=k\Rightarrow\left\{{}\begin{matrix}a=3k\\b=4k\end{matrix}\right.\)

Có: \(a.b=48\)

=> \(3k.4k=48\)

=> \(12k^2=48\)

=> \(k^2=48:12\)

=> \(k^2=4\)

=> \(k=\pm2.\)

TH1: \(k=2.\)

\(\Rightarrow\left\{{}\begin{matrix}a=2.3=6\\b=2.4=8\end{matrix}\right.\)

TH2: \(k=-2.\)

\(\Rightarrow\left\{{}\begin{matrix}a=\left(-2\right).3=-6\\b=\left(-2\right).4=-8\end{matrix}\right.\)

Vậy \(\left(a;b\right)=\left(6;8\right),\left(-6;-8\right).\)

Chúc bạn học tốt!