\(11,\\ a,=4\cdot5+14:7=20+2=22\\ b,=3\sqrt{2}-12\sqrt{2}+5\sqrt{2}=-4\sqrt{2}\\ c,=\dfrac{3-\sqrt{2}+3+\sqrt{2}}{\left(3-\sqrt{2}\right)\left(3+\sqrt{2}\right)}=\dfrac{6}{7}\\ 12,\\ a,P=\dfrac{\sqrt{x}+3+\sqrt{x}-3}{\left(\sqrt{x}-3\right)\left(\sqrt{x}+3\right)}\cdot\dfrac{\sqrt{x}-3}{\sqrt{x}}\\ P=\dfrac{2\sqrt{x}}{\sqrt{x}\left(\sqrt{x}+3\right)}=\dfrac{2}{\sqrt{x}+3}\\ b,P=\dfrac{1}{2}\Leftrightarrow\sqrt{x}+3=4\Leftrightarrow x=1\left(tm\right)\)
a: \(=4\cdot5+14:7=20+2=22\)
b: \(=3\sqrt{2}-8\sqrt{2}+5\sqrt{2}=0\)
\(14,\\ ĐK:x\ge2\\ PT\Leftrightarrow\sqrt{\left(x-1\right)\left(x-2\right)}+\sqrt{x+3}=\sqrt{x-2}+\sqrt{\left(x+3\right)\left(x-1\right)}\)
Đặt \(\left\{{}\begin{matrix}\sqrt{x-1}=a\\\sqrt{x-2}=b\\\sqrt{x+3}=c\end{matrix}\right.\left(a,b,c\ge0\right)\), PTTT:
\(ab+c=b+ac\\ \Leftrightarrow a\left(b-c\right)-\left(b-c\right)=0\\ \Leftrightarrow\left(a-1\right)\left(b-c\right)=0\\ \Leftrightarrow\left[{}\begin{matrix}a=1\\b=c\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x-1=1\\x-2=x+3\end{matrix}\right.\Leftrightarrow\left[{}\begin{matrix}x=2\left(tm\right)\\0x=5\left(ktm\right)\end{matrix}\right.\\ \Leftrightarrow x=2\)
a) = 4.5 + 14:7 = 20 + 2 = 22
b) = \(3\sqrt{2}-12\sqrt{2}+5\sqrt{2}=-4\sqrt{2} \)
c) =\(\dfrac{3-\sqrt{2}+3+\sqrt{2}}{(3-\sqrt{2}).(3+\sqrt{2})} \)\(=\dfrac{6}{9-2}=\dfrac{6}{7} \)
