\(5,\\ K=\sqrt{5x-9+6\sqrt{5x-9}+9}+\sqrt{5x-9-6\sqrt{5x-9}+9}\\ K=\sqrt{\left(\sqrt{5x-9}+3\right)^2}+\sqrt{\left(\sqrt{5x-9}-3\right)^2}\\ K=\sqrt{5x-9}+3+\sqrt{5x-9}-3=2\sqrt{5x-9}\ge0,\forall x\\ K_{min}=0\Leftrightarrow\sqrt{5x-9}=0\Leftrightarrow x=\dfrac{9}{5}\)
\(3,\\ 1,A=\dfrac{1,44+7}{\sqrt{1,44}}=\dfrac{7,44}{1,2}=\dfrac{31}{5}\\ 2,B=\dfrac{x-3\sqrt{x}+\left(2\sqrt{x}-1\right)\left(\sqrt{x}+3\right)-2x+\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\\ B=\dfrac{x-3\sqrt{x}+2x+5\sqrt{x}-3-2x+\sqrt{x}+3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\\ B=\dfrac{\sqrt{x}\left(\sqrt{x}-3\right)}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}=\dfrac{\sqrt{x}}{\sqrt{x}+3}\)
\(3,S=\dfrac{1}{B}+A=\dfrac{\sqrt{x}+3}{\sqrt{x}}+\dfrac{x+7}{\sqrt{x}}=\dfrac{x+\sqrt{x}+10}{\sqrt{x}}\\ S=\sqrt{x}+1+\dfrac{10}{\sqrt{x}}\ge2\sqrt{\sqrt{x}\cdot\dfrac{10}{\sqrt{x}}}+1=2\sqrt{10}+1\left(BĐT.cosi\right)\)
Dấu \("="\Leftrightarrow x=10\)
\(1,HC=BC-HB=6\left(cm\right)\)
Áp dụng HTL:
\(\left\{{}\begin{matrix}AB^2=BH\cdot BC=16\\AC^2=CH\cdot BC=48\\AH^2=BH\cdot HC=12\end{matrix}\right.\Rightarrow\left\{{}\begin{matrix}AB=4\left(cm\right)\\AC=4\sqrt{3}\left(cm\right)\\AH=2\sqrt{3}\left(cm\right)\end{matrix}\right.\)
\(2,\widehat{ADB}=\widehat{AHB}\left(=90^0\right)\) nên \(ADHB\) nội tiếp
\(\Rightarrow\widehat{HDB}=\widehat{HAB}\left(cùng.chắn.HB\right)\)
Mà \(\widehat{HAB}=\widehat{ACB}\left(cùng.phụ.\widehat{HAC}\right)\)
\(\Rightarrow\widehat{HDB}=\widehat{ACB}\)
\(\left\{{}\begin{matrix}\widehat{HDB}=\widehat{ACB}\left(cm.trên\right)\\\widehat{KBC}.chung\end{matrix}\right.\Rightarrow\Delta BHD\sim\Delta BKC\left(g.g\right)\\ \Rightarrow\dfrac{BD}{BC}=\dfrac{BH}{BK}\Rightarrow BD\cdot BK=BH\cdot BC\)
\(c,\) Áp dụng công thức tính diện tích hình tam giác bằng
giải giúp em bài 11 12 13 của bài 14 đi ạ
