Câu 3:
a) \(VT=3+4+4\sqrt{3}+3+4-4\sqrt{3}=14=VP\)
b) \(pt\Leftrightarrow\sqrt{\left(x-3\right)^2}=6\)
\(\Leftrightarrow\left|x-3\right|=6\)
\(\Leftrightarrow\left[{}\begin{matrix}x-3=6\\x-3=-6\end{matrix}\right.\)\(\Leftrightarrow\left[{}\begin{matrix}x=9\\x=-3\end{matrix}\right.\)
Bài 4:
a) ĐKXĐ: \(x\ge0,x\ne1\)
\(P=\dfrac{\left(\sqrt{x}+1\right)^2}{\sqrt{x}+1}+\dfrac{\left(\sqrt{x}-1\right)\left(\sqrt{x}+1\right)}{\sqrt{x}-1}-3\)
\(=\sqrt{x}+1+\sqrt{x}+1-3=2\sqrt{x}-1\)
b) \(P=2\sqrt{x}-1=2.\sqrt{1+\dfrac{\sqrt{3}}{2}}-1\)
\(=2.\sqrt{\dfrac{2+\sqrt{3}}{2}}-1=2.\sqrt{\dfrac{4+2\sqrt{3}}{4}}-1\)
\(=2.\dfrac{\sqrt{\left(\sqrt{3}+1\right)^2}}{2}-1=\sqrt{3}+1-1=\sqrt{3}\)
