Question

tìm các số a b biết 3/5a=2/3b và a^2=b^2=38

Answer 1

Ta có: \(\dfrac{3}{5}a=\dfrac{2}{3}b\)

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

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

\(\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{5}{3}k\\b=\dfrac{3}{2}k\end{matrix}\right.\)

Ta có: \(a^2-b^2=38\)

\(\Leftrightarrow k^2\cdot\dfrac{25}{9}-k^2\cdot\dfrac{9}{4}=38\)

\(\Leftrightarrow k^2=72\)

Trường hợp 1: \(k=6\sqrt{2}\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{5}{3}k=10\sqrt{2}\\b=\dfrac{3}{2}k=9\sqrt{2}\end{matrix}\right.\)

Trường hợp 2: \(k=-6\sqrt{2}\)

\(\Leftrightarrow\left\{{}\begin{matrix}a=\dfrac{5}{3}k=-10\sqrt{2}\\b=\dfrac{3}{2}k=-9\sqrt{2}\end{matrix}\right.\)