\((3\sqrt{20}-2\sqrt{80}+\frac{2}{3}\sqrt{45}-\sqrt{5}):\sqrt{5}\)
\(=\left(3\sqrt{2^2.5}-2\sqrt{4^2.5}+\frac{2}{3}\sqrt{3^2.5}-\sqrt{5}\right):\sqrt{5}\)
\(=\left(3.2\sqrt{5}-2.4\sqrt{5}+\frac{2}{3}.3\sqrt{5}\right):\sqrt{5}\)
\(=\left(6\sqrt{5}-8\sqrt{5}+2\sqrt{5}-\sqrt{5}\right):\sqrt{5}\)
\(=-\sqrt{5}:\sqrt{5}=-1\)
\(\left(\frac{2+\sqrt{5}}{2-\sqrt{5}}-\frac{2-\sqrt{5}}{2+\sqrt{5}}\right).\frac{5-\sqrt{5}}{1-\sqrt{5}}\)
\(=\left(\frac{\left(2+\sqrt{5}\right)^2}{\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)}-\frac{\left(2-\sqrt{5}\right)^2}{\left(2-\sqrt{5}\right)\left(2+\sqrt{5}\right)}\right).\frac{\sqrt{5}\left(\sqrt{5}-1\right)}{1-\sqrt{5}}\)
\(=\left(\frac{4+4\sqrt{5}+5-\left(4-4\sqrt{5}+5\right)}{4-5}\right).\frac{-\sqrt{5}\left(1-\sqrt{5}\right)}{1-\sqrt{5}}\)
\(=\frac{9+4\sqrt{5}-9+4\sqrt{5}}{-1}.\left(-\sqrt{5}\right)\)
\(-8\sqrt{5}.\left(-\sqrt{5}\right)=40\)
Câu này để t nghĩ xem nào :v
Câu này viết cả kia ra à???
\(B=\frac{3x+1}{x^2-2x+1}=\frac{3x+1}{\left(x-1\right)^2}\left(đkxđ:x\ne1\right)\)
Có:
\(B=\frac{3x+1}{x^2-2x+1}\)
\(B=\frac{3x+1}{\left(x-1^2\right)}\)
\(B=\frac{3\left(x-1\right)}{\left(x-1\right)^2}+\frac{4}{\left(x-1\right)^2}\)
\(B=\frac{3}{x-1}+\frac{4}{\left(x-1\right)^2}\)
Đặt \(\frac{1}{x-1}=y\)
\(\Rightarrow B=3y+4y^2\)
\(\Rightarrow B=\left(2y\right)^2+2.2y.\frac{3}{4}+\left(\frac{3}{4}\right)^2-\frac{9}{16}\)
\(\Rightarrow B=-\frac{9}{16}+\left(2y+\frac{3}{4}\right)^2\ge-\frac{9}{16}\)
Vì \(\left(2y+\frac{3}{4}\right)^2\ge0\forall y\)
\(\Rightarrow B_{min}=-\frac{9}{16}\)
\(\Leftrightarrow\left(2y+\frac{3}{4}\right)^2=0\)
\(\Leftrightarrow2y+\frac{3}{4}=0\)
\(\Leftrightarrow y=-\frac{3}{8}\)
\(\Leftrightarrow\frac{1}{x-1}=-\frac{3}{8}\)
\(\Leftrightarrow-3\left(x-1\right)=8\)
\(\Leftrightarrow x=-\frac{5}{3}\)
Vậy A đạt gtnn khi x=\(-\frac{5}{3}\)
