Question

\(\sqrt{2x^2+21x-11}-\sqrt{2x^2-9x+4}=\sqrt{18x-9}\)

Answer 1

ĐKXĐ: ..

Đặt \(\left\{{}\begin{matrix}\sqrt{2x^2+21x-11}=a\\\sqrt{2x-1}=b\end{matrix}\right.\)

\(a-\sqrt{a^2-15b^2}=b\)

\(\Leftrightarrow a-b=\sqrt{a^2-15b^2}\) (\(a\ge b\))

\(\Rightarrow a^2-2ab+b^2=a^2-15b^2\)

\(\Leftrightarrow8b^2-ab=0\)

\(\Leftrightarrow\left[{}\begin{matrix}b=0\\a=8b\end{matrix}\right.\) \(\Rightarrow\left[{}\begin{matrix}2x-1=0\\\sqrt{2x^2+21x-11}=8\sqrt{2x-1}\end{matrix}\right.\)

\(\Leftrightarrow\left[{}\begin{matrix}2x-1=0\\2x^2+21x-11=64\left(2x-1\right)\end{matrix}\right.\)