c) \(\sqrt{x^2-4}+\sqrt{x^2+4x+4}=0\)
\(\Leftrightarrow\sqrt{x^2-4}+\sqrt{\left(x+2\right)^2}=0\)
\(\Leftrightarrow\sqrt{\left(x-2\right)\left(x+2\right)}+\left(x+2\right)=0\)
\(\Leftrightarrow\sqrt{x+2}\left(\sqrt{x-2}+1\right)=0\)
\(\Leftrightarrow\sqrt{x+2}=0\)
\(\Leftrightarrow x=-2\)
Bạn tự tìm ĐK nha
a) \(\sqrt{x-2\sqrt{x-1}}=3\)
\(\Leftrightarrow\sqrt{x-1-2\sqrt{x-1}+1}=3\)
\(\Leftrightarrow\sqrt{\left(\sqrt{x-1}-1\right)^2}=3\)
\(\Leftrightarrow\left|\sqrt{x-1}-1\right|=3\)
\(\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}-1=3\\\sqrt{x-1}-1=-3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}\sqrt{x-1}=4\\\sqrt{x-1}=-2\left(l\right)\end{matrix}\right.\)
\(\Leftrightarrow x-1=16\Leftrightarrow x=17\)
b) \(\sqrt{x^4-2x^2+1}=x-1\)ĐK : \(x\ge1\)
\(\Leftrightarrow\sqrt{\left(x^2-1\right)^2}=x-1\)
\(\Leftrightarrow x^2-1=x-1\)
\(\Leftrightarrow x\left(x-1\right)=0\)
\(\Leftrightarrow\left[{}\begin{matrix}x=0\\x=1\end{matrix}\right.\)
a)
\(\sqrt{x-2\sqrt{x-1}}=3\\ \Leftrightarrow\sqrt{x-2\sqrt{x-1}}^2=3^2\\ \Leftrightarrow x-2\sqrt{x-1}=9\\ \Leftrightarrow-2\sqrt{x-1}=9-x\\ \Leftrightarrow\left(-2\sqrt{x-1}\right)^2=\left(9-x\right)^2\\ \Leftrightarrow4\left(x-1\right)=81-18x+x^2\\ \Leftrightarrow4x-4=81-18x+x^2\\ \Leftrightarrow22x-85-x^2=0\\ \Leftrightarrow x^2-22x+85=0\\ \Leftrightarrow\left(x^2-17x\right)-\left(5x-85\right)=0\\ \Leftrightarrow x\left(x-17\right)-5\left(x-17\right)=0\\ \Leftrightarrow x=17;x=5\)
Thử nghiệm => x = 17
c)
\(\sqrt{x^2-4}+\sqrt{x^2+4x+4}=0\\ \Leftrightarrow\sqrt{x^2-4}=-\sqrt{x^2+4x+4}\\ \Leftrightarrow x^2-4=x^2+4x+4\\ \Leftrightarrow-4x=8\\ \Leftrightarrow x=-2\)
Thử nghiệm => x = -2
