Question

Giải pt

a)\(\sqrt{x^2-16}-3\sqrt{x-4}=0\)

b)\(\sqrt{3x^2-4x}=2x-3\)

Answer 1

a) \(\sqrt{x^2-16}-3\sqrt{x-4}=0\)

\(\Leftrightarrow\sqrt{x^2-16}=3\sqrt{x-4}\)

\(\Leftrightarrow\sqrt{x^2-16}=\sqrt{9x-36}\)

\(\Leftrightarrow x^2-16=9x-36\)

\(\Leftrightarrow\left(x-4\right)\left(x+4\right)-9x+36=0\)

\(\Leftrightarrow\left(x-4\right)\left(x+4\right)-9\left(x-4\right)=0\)

\(\Leftrightarrow\left(x-4\right)\left(x-5\right)=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x-4=0\\x-5=0\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=4\\x=5\end{matrix}\right.\)

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