Question

Giải phương trình: \(\sqrt{x-1-2\sqrt{x-2}}+\sqrt{x+7+6\sqrt{x-2}}=2\)

Answer 1

<=> \(\sqrt{\left(x-2\right)-2\sqrt{x-2}+1}+\sqrt{\left(x-2\right)+6\sqrt{x-2}+9}=2\)    (đkxđ x\(\ge2\))

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

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

dễ thấy VT \(\ge\)2   =VP  (vì l\(1-\sqrt{x-2}\)l \(\ge\)\(1-\sqrt{x-2}\))

=> VT = VP    <=> l\(1-\sqrt{x-2}\)l = \(1-\sqrt{x-2}\)

<=> \(1-\sqrt{x-2}\ge0\) 

<=> \(\sqrt{x-2}\le1\)

=> x-2 \(\le\)1

<=> x\(\le\)3

kh với đkxđ => \(2\le x\le3\)