Hãy nhập câu hỏi của bạn vào đây, nếu là tài khoản VIP, bạn sẽ được ưu tiên trả lời.
\(x+3\sqrt{x+2}-2\)
\(=x+2+3\sqrt{x+2}-4\)
\(=\left(\sqrt{x+2}\right)^2+4\sqrt{x+2}-\sqrt{x+2}-4\)
\(=\left(\sqrt{x+2}+4\right)\left(\sqrt{x+2}-1\right)\)
\(x+3\sqrt{x+2}-2=x+2+3\sqrt{x+2}-4\)
\(=x+2-\sqrt{x+2}+4\sqrt{x+2}-4\)
\(=\sqrt{x+2}\left(\sqrt{x+2}-1\right)+4\left(\sqrt{x+2}-1\right)\)
\(=\left(\sqrt{x+2}-1\right)\left(\sqrt{x+2}+4\right)\)
\(x+2\sqrt{x-1}=\left(x-1\right)+2\sqrt{x-1}+1=\left(\sqrt{x-1}+1\right)^2\)
\(x-4\sqrt{x-2}+2=\left(x-2\right)-4\sqrt{x-2}+4=\left(\sqrt{x-2}-2\right)^2\)
\(x+2\sqrt{x-1}=\left(\sqrt{x-1}+1\right)^2\)
\(x-4\sqrt{x-2}+2=\left(\sqrt{x-2}+4\right)^2\)
Lời giải:
$x-2\sqrt{x}-15=(x-5\sqrt{x})+(3\sqrt{x}-15)$
$=\sqrt{x}(\sqrt{x}-5)+3(\sqrt{x}-5)=(\sqrt{x}-5)(\sqrt{x}+3)$
\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=2+\sqrt{3}+\sqrt{6}+2\sqrt{2}\)
\(=2+\sqrt{3}+\sqrt{2}\left(2+\sqrt{3}\right)=\left(2+\sqrt{3}\right)\left(\sqrt{2}+1\right)\)
\(2+\sqrt{3}+\sqrt{6}+\sqrt{8}=\left(\sqrt{2}+1\right)\left(2+\sqrt{3}\right)\)
\(=\left(x+\sqrt{2}\right)^2\)
(x+√2)^2