Question

Thach thuc danh hai

\(\sqrt{\left(2x+4+6\sqrt{2-5}\right)}+\sqrt{\left(2x-4+2\sqrt{2x-5}\right)}\)  \(=4\)

Tim x

Answer 1

Đề đúng: \(\sqrt{2x+4+6\sqrt{2x-5}}+\sqrt{2x-4+2\sqrt{2x-5}}=4\)

ĐK: \(x\ge\frac{5}{2}\)

Pt trên tương đương: \(\sqrt{2x-5+6\sqrt{2x-5}+9}+\sqrt{2x-5+2\sqrt{2x-5}+1}=4\)

<=>\(\sqrt{\left(\sqrt{2x-5}+3\right)^2}+\sqrt{\left(\sqrt{2x-5}+1\right)^2}=4\)

<=>\(\sqrt{2x-5}+3+\sqrt{2x-5}+1=4\)

<=>\(2\sqrt{2x-5}=0\Leftrightarrow2x-5=0\Leftrightarrow x=\frac{5}{2}\left(\text{nhận}\right)\)

Vậy S={5/2}