Question

Giải phương trình

\(\frac{\sqrt{2\left(x^2-16\right)}}{\sqrt{x-3}}+\sqrt{x-3}=\frac{7-x}{\sqrt{x-3}}\)

Answer 1

ĐKXĐ: \(x\ge4\)

\(\Leftrightarrow\sqrt{2\left(x^2-16\right)}+x-3=7-x\)

\(\Leftrightarrow\sqrt{2\left(x^2-16\right)}=10-2x\) (\(x\le5\))

\(\Leftrightarrow2\left(x^2-16\right)=\left(10-2x\right)^2\)

\(\Leftrightarrow x^2-20x+66=0\)

\(\Leftrightarrow\left[{}\begin{matrix}x=10+\sqrt{34}>5\left(l\right)\\x=10-\sqrt{34}\end{matrix}\right.\)