Question

tìm a, b, c biết: \(\dfrac{a}{5}=\dfrac{b}{3}=\dfrac{c}{2}và\) ab=\(c^2+11\)

Answer 1

Từ ab = c² + 11 suy ra ab - c² = 11.

Ta có:

\(\dfrac{a}{5}=\dfrac{b}{3}=\dfrac{c}{2}\)

\(\Rightarrow\dfrac{ab}{15}=\dfrac{c^2}{4}\)

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

\(\dfrac{ab}{15}=\dfrac{c^2}{4}=\dfrac{ab-c^2}{15-4}=\dfrac{11}{11}=1\)

\(\Rightarrow\left\{{}\begin{matrix}ab=15\\c^2=4\Rightarrow c=\pm2\end{matrix}\right.\)

+) Nếu c = 2 thì \(\dfrac{a}{5}=\dfrac{b}{3}=1\Rightarrow\left\{{}\begin{matrix}a=5\\b=3\end{matrix}\right.\) (thỏa mãn)

+) Nếu c = -2 thì \(\dfrac{a}{5}=\dfrac{b}{3}=-1\Rightarrow\left\{{}\begin{matrix}a=-5\\b=-3\end{matrix}\right.\) (thỏa mãn)

Vậy (a, b) \(\in\left\{\left(5;3\right),\left(-5;-3\right)\right\}\)