Question

Tìm số hữu tỉ a, b thoả mãn đẳng thức: \(\sqrt{3a\sqrt{3}}-\sqrt{b\sqrt{3}}=\sqrt{2\sqrt{3}-3}\)

Answer 1

Bình phương 2 vế ta được :

\(3a\sqrt{3}-2\sqrt{9ab}+b\sqrt{3}=2\sqrt{3}-3\)

\(\Leftrightarrow\left(3a+b\right)\sqrt{3}-6\sqrt{ab}=2\sqrt{3}-3\)

\(\Leftrightarrow\left\{{}\begin{matrix}3a+b=2\\6\sqrt{ab}=3\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}3a+b=2\\ab=\dfrac{1}{4}\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}a=\dfrac{1}{2}\\b=\dfrac{1}{2}\end{matrix}\right.\)