Question

\(\sqrt{x-1+4\sqrt{x-5}}+\sqrt{x-1-4\sqrt{x-5}}=2\left(x-17\right)\)

Answer 1

\(\sqrt{x-5+4\sqrt{x-5}+4}+\sqrt{x-5-4\sqrt{x-5}+4}=2\left(x-17\right)\)

⇔ \(\sqrt{\left(\sqrt{x-5}+4\right)^2}+\sqrt{\left(\sqrt{x-5}-4\right)^2}=2\left(x-17\right)\)

⇔ \(\left|\sqrt{x-5}+4\right|+\left|\sqrt{x-5}-4\right|=2\left(x-17\right)\) (1)

Do \(x\ge17\) nên từ (1) suy ra \(2\sqrt{x-5}=2\left(x-17\right)\)

⇔ \(x-5-\sqrt{x-5}-12=0\)

⇔ \(\left[{}\begin{matrix}\sqrt{x-5}=4\\\sqrt{x-5}=-3\end{matrix}\right.\)⇔ \(x=21\) (t/m)