Câu 1:
\(a,=\dfrac{7+4\sqrt{3}-\left(7-4\sqrt{3}\right)}{\left(\sqrt{3}-2\right)\left(\sqrt{3}+2\right)}+\dfrac{8\sqrt{3}\left(\sqrt{2}-1\right)}{\sqrt{2}-1}=-8\sqrt{3}+8\sqrt{3}=0\\ b,=5\sqrt{6}\left(4\sqrt{6}+10\sqrt{6}-35\sqrt{6}\right)\\ =5\sqrt{6}\cdot\left(-21\right)\sqrt{6}=-630\)
Câu 2:
\(a,\Leftrightarrow3\left|x-1\right|=12\Leftrightarrow\left|x-1\right|=4\Leftrightarrow\left[{}\begin{matrix}x=4+1=5\\x=-4+1=-3\end{matrix}\right.\\ b,ĐK:x\ge2\\ PT\Leftrightarrow\left\{{}\begin{matrix}2x+5=0\\2x-4=0\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}x=-\dfrac{5}{2}\\x=2\end{matrix}\right.\left(vô.lí\right)\\ \Leftrightarrow x\in\varnothing\)
Câu 3:
\(a,C=\left(\dfrac{3}{\sqrt{1+x}}+\sqrt{1-x}\right):\dfrac{32+\sqrt{1-x^2}}{\sqrt{\left(1-x\right)\left(1+x\right)}}\left(-1< x< 1\right)\\ C=\dfrac{3+\sqrt{1-x^2}}{\sqrt{\left(1-x\right)\left(1+x\right)}}\cdot\dfrac{\sqrt{\left(1-x\right)\left(1+x\right)}}{32+\sqrt{1-x^2}}=\dfrac{3+\sqrt{1-x^2}}{32+\sqrt{1-x^2}}\\ b,C=\dfrac{1}{2}\Leftrightarrow\dfrac{3+\sqrt{1-x^2}}{32+\sqrt{1-x^2}}=\dfrac{1}{2}\\ \Leftrightarrow6+2\sqrt{1-x^2}=32+\sqrt{1-x^2}\\ \Leftrightarrow\sqrt{1-x^2}=26\\ \Leftrightarrow1-x^2=676\\ \Leftrightarrow x^2=-675\\ \Leftrightarrow x\in\varnothing\)
Câu 2:
a: \(\Leftrightarrow\left|x-1\right|=4\)
\(\Leftrightarrow\left[{}\begin{matrix}x-1=4\\x-1=-4\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=5\\x=-3\end{matrix}\right.\)