Question

Tìm a ; b ; c biết

\(a^2+3b^2-2c^2=\left(-16\right)và\dfrac{a}{2}=\dfrac{b}{3}=\dfrac{c}{4}\)

Answer 1

Giải:

Đặt \(\frac{a}{2}=\frac{b}{3}=\frac{c}{4}=k\Rightarrow\left\{\begin{matrix}a=2k\\b=3k\\c=4k\end{matrix}\right.\)

Ta có: \(a^2+3b^2-2c^2=\left(-16\right)\)

\(\Rightarrow4k^2+27k^2-32k^2=-16\)

\(\Rightarrow\left(-1\right)k^2=-16\)

\(\Rightarrow k^2=16\)

\(\Rightarrow k=\pm4\)

+) \(k=4\Rightarrow a=8;b=12;c=16\)

+) \(k=-4\Rightarrow a=-8;b=-12;c=-16\)

Vậy bộ số \(\left(x;y;z\right)\) là \(\left(8;12;16\right);\left(-8;-12;-16\right)\)