P = \(\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}=\sqrt{x-1-2\sqrt{x-1}+1}+\sqrt{x-1+2\sqrt{x-1}+1}\)
\(=\sqrt{\left(\sqrt{x-1}-1\right)^2}+\sqrt{\left(\sqrt{x-1}+1\right)^2}=l\sqrt{x-1}-1l+l\sqrt{x-1}+1l\)
Vì căn x - 1 > = 0 => căn x - 1 +1 > 0 => l căn x + 1 l + 1 =căn (x - 1) + 1
(+) lCĂn ( x - 1) - 1 l = căn (x - 1) - 1 khi căn (x - 1) - 1 >= 0 => x >= 2 ta có :
căn ( x- 1) - 1 + căn ( x- 1 ) + 1 = 2 căn ( x - 1)
(+) l căn ( x- 1) - 1 l = 1- căn ( x - 1) khi 0 < x< 2 thay vòa bt ta có ( tự làm tiếp nha)
Đúng cho mình đó nhe
ĐKXĐ:
\(x-1\ge0\)và \(x-2\sqrt{x-1}\ge0\)
<=>\(x\ge1\)và\(x\ge2\sqrt{x-1}\)
<=>\(x\ge1\)và \(x^2\ge4x-4\)
<=>\(x\ge1\)và \(\left(x-4\right)^2\ge0\)( luôn đúng với mọi x)
<=> \(x\ge1\)
\(P=\sqrt{x-2\sqrt{x-1}}+\sqrt{x+2\sqrt{x-1}}\)
\(=\sqrt{x-1-2\sqrt{x-1}+1}+\sqrt{x-1+2\sqrt{x-1}+1}\)
\(=\sqrt{\left(\sqrt{x-1}-1\right)^2}+\sqrt{\left(\sqrt{x-1}+1\right)^2}\)
\(=\left|\sqrt{x-1}-1\right|+\left|\sqrt{x-1}+1\right|\)
nếu \(\sqrt{x-1}-1\le0\)thì
\(P=1-\sqrt{x-1}+\sqrt{x-1}+1=2\)
nếu \(\sqrt{x-1}-1\ge0\)thì:
\(P=\sqrt{x-1}-1+\sqrt{x-1}+1=2\sqrt{x-1}\)
