Bài 1:
a: \(=\left(5\sqrt{3}-4\sqrt{3}-\sqrt{2}\right)\left(\sqrt{3}+\sqrt{2}\right)=1\)
b: \(=\dfrac{6-2\sqrt{5}-3-3\sqrt{5}}{4}+\dfrac{3\sqrt{5}}{4}=\dfrac{3-2\sqrt{5}}{4}\)
1.
a, \(\left(\sqrt{75}-\sqrt{2}-\sqrt{48}\right)\left(\sqrt{2}+\sqrt{3}\right)\)
\(=\left(5\sqrt{3}-\sqrt{2}-4\sqrt{3}\right)\left(\sqrt{2}+\sqrt{3}\right)\)
\(=\left(\sqrt{3}-\sqrt{2}\right)\left(\sqrt{2}+\sqrt{3}\right)\)
\(=3-2=1\)
1.
b, \(\dfrac{3-\sqrt{5}}{3+\sqrt{5}}-\dfrac{3}{3-\sqrt{5}}+\dfrac{45}{4\sqrt{5}}\)
\(=\dfrac{\left(3-\sqrt{5}\right)^2}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}-\dfrac{3\left(3+\sqrt{5}\right)}{\left(3+\sqrt{5}\right)\left(3-\sqrt{5}\right)}+\dfrac{45}{4\sqrt{5}}\)
\(=\dfrac{14-6\sqrt{5}-9-3\sqrt{5}}{9-5}+\dfrac{45}{4\sqrt{5}}\)
\(=\dfrac{5-9\sqrt{5}}{4}+\dfrac{9\sqrt{5}}{4}\)
\(=\dfrac{5}{4}\)
Bài 2:
\(a,ĐK:x\ge-1\\ PT\Leftrightarrow3\sqrt{x+1}=2\sqrt{x+1}+5\\ \Leftrightarrow\sqrt{x+1}=5\\ \Leftrightarrow x+1=25\\ \Leftrightarrow x=24\left(tm\right)\\ b,\Leftrightarrow\left|3x-1\right|=2\Leftrightarrow\left[{}\begin{matrix}3x-1=2\\1-3x=2\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
Bài 3:
\(b,\text{PT hoành độ giao điểm: }x+2=-2x-1\Leftrightarrow x=-1\Leftrightarrow y=1\Leftrightarrow A\left(-1;1\right)\\ \text{Vậy }A\left(-1;1\right)\text{ là giao 2 đths}\\ c,\Leftrightarrow\left\{{}\begin{matrix}-a+b=0\\a=-2;b\ne-1\end{matrix}\right.\Leftrightarrow\left\{{}\begin{matrix}a=-2\\b=-2\end{matrix}\right.\Leftrightarrow\left(D_3\right):y=-2x-2\)
2.
a, ĐK: \(x\ge-1\)
\(\sqrt{9x+9}=4\sqrt{\dfrac{x+1}{4}}+5\)
\(\Leftrightarrow3\sqrt{x+1}=2\sqrt{x+1}+5\)
\(\Leftrightarrow\sqrt{x+1}=5\)
\(\Leftrightarrow x+1=25\)
\(\Leftrightarrow x=24\left(tm\right)\)
2.
b, ĐK: \(x\in R\)
\(\sqrt{9x^2-6x+1}=2\)
\(\Leftrightarrow\sqrt{\left(3x-1\right)^2}=2\)
\(\Leftrightarrow\left|3x-1\right|=2\)
\(\Leftrightarrow\left[{}\begin{matrix}3x-1=2\\3x-1=-2\end{matrix}\right.\)
\(\Leftrightarrow\left[{}\begin{matrix}x=1\\x=-\dfrac{1}{3}\end{matrix}\right.\)
